Edit Profile (opens in new tab) Vodop’yanov, Sergeĭ Konstantinovich Compute Distance To: Compute Author ID: vodopyanov.serguei-k Published as: Vodop’yanov, S. K.; Vodopyanov, S. K.; Vodopyanov, Sergey; Vodop’janov, S. K.; Vodop’janov, Sergei Konstantinovitch; Vodop’yanov, Serguei K.; Vodop’yanov, Sergej K.; Vodop’yanov, Serguei; Vodop’yanov, Sergei; Vodop’yanov, Sergey; Vodop’janov, Serge; Vodopjanov, S. K.; Vodopyanov, S. more...less External Links: MGP · Math-Net.Ru Documents Indexed: 168 Publications since 1970, including 1 Book 6 Contributions as Editor Co-Authors: 111 Co-Authors with 104 Joint Publications 2,025 Co-Co-Authors all top 5 Co-Authors 67 single-authored 14 Gol’dshtejn, Vladimir M. 12 Ukhlov, Alexander Dadar-Oolovich 10 Reshetnyak, Yuriĭ Grigor’evich 9 Kutateladze, Semën Samsonovich 7 Karmanova, Maria B. 7 Markina, Irina 7 Pupyshev, I. M. 6 Greshnov, Aleksandr Valer’evich 6 Isangulova, D. V. 6 Taimanov, Iskander Asanovich 4 Evseev, Nikita Aleksandrovich 4 Gordon, Evgeniĭ Izrail’evich 4 Kudryavtseva, N. A. 4 Latfullin, T. G. 4 Molchanova, Anastasia Olegovna 3 Gutman, Aleksandr Efimovich 3 Kusraev, Anatoly Georgievich 3 Vesnin, Andrei Yu. 2 Bokut, Leonid A. 2 Gol’dshtein, Vladimir Mikhailovich 2 Kondakov, Vladimir Petrovich 2 Malyugin, Sergey Artem’evich 2 Muzaev, Illarion Davidovich 2 Romanov, Aleksandr Sergeevich 2 Romanovskii, N. N. 2 Selivanova, Svetlana V. 2 Tyulenev, Alexander I. 2 Valiev, Mars K. 1 Abanin, Aleksandr Vasil’evich 1 Alborova, M. S. 1 Alexandrov, Victor A. 1 Arkhangel’skiĭ, Dmitriĭ A. 1 Avkhadiev, Farit Gabidinovich 1 Baizhanov, Bektur Sembiuly 1 Basaeva, Elena K. 1 Basalaev, S. G. 1 Baykin, Alekseĭ N. 1 Belegradek, Oleg V. 1 Belyaev, V. Ya. 1 Beresmovskiĭ, V. N. 1 Botvinnik, V. A. 1 Boyarskij, Yu. I. 1 Burenkov, Viktor Ivanovich 1 Chernikov, V. M. 1 Chirka, Evgeni M. 1 Daderkin, Dmitri O. 1 Dekhtyar, Alexander M. 1 Demidenko, Gennadiĭ Vladimirovich 1 Dikovsky, Alexander Yakovlevich 1 Dubinin, Vladimir N. 1 Dudakov, Sergey M. 1 Gitik, Moti 1 Gol’dshteyn, V. M. 1 Gol’dstein, Vladimir Mikailovitch 1 Goryainov, Viktor V. 1 Grigor’yan, Alexander Asaturovich 1 Gurevich, Yuri 1 Iwaniec, Tadeusz 1 Jain, Pankaj 1 Karmanova, M. V. 1 Kesel’man, V. M. 1 Khudalov, Marat Zakharovich 1 Klimentov, Sergeĭ Borisovich 1 Klyachin, Vladimir Aleksandrovich 1 Koibaev, Vladimir Amurkhanovich 1 Kononenko, L. J. 1 Konylov, Ya. A. 1 Kopfer, A. V. 1 Koptev, Aleksandr Viktorovich 1 Kopycov, A. P. 1 Kopylov, Anatoliĭ Pavlovich 1 Korobeĭnik, Yuriĭ Fëdorovich 1 Krushkal, Samuel L. 1 Kutatetadse, S. S. 1 Kuz’minov, Vladimir I. 1 Kysmunych, A. V. 1 Loboda, Alexander Vasil’evich 1 Ludnik, V. G. 1 Martio, Olli 1 Matiyasevich, Yuriĭ Vladimirovich 1 Mints, Grigoriĭ Efroimovich 1 Musikaev, Ilmir Kh. 1 Novikov, Sergeĭ Petrovich 1 Pelikh, V. I. 1 Pinchuk, Sergey 1 Rebrov, A. K. 1 Reshetnyakh, Yu. G. 1 Rodionov, Evgeniĭ Dmitrievich 1 Rylov, A. I. 1 Sabitov, Idzhad Khakovich 1 Semënov, Alekseĭ L’vovich 1 Sergeev, Armen Glebovich 1 Singh, Monika 1 Slavskiĭ, Viktor Vladimirovich 1 Sobolev, Sergeĭ L’vovich 1 Stolboushkin, Alexei P. 1 Tarusov, V. B. 1 Tasoev, Batradz Botazovich 1 Tkachev, Vladimir G. 1 Tomilov, A. O. ...and 12 more Co-Authors all top 5 Serials 38 Doklady Mathematics 34 Siberian Mathematical Journal 17 Sibirskiĭ Matematicheskiĭ Zhurnal 8 Soviet Mathematics. Doklady 7 Vladikavkazskiĭ Matematicheskiĭ Zhurnal 5 Matematicheskie Trudy 4 Siberian Advances in Mathematics 3 Russian Mathematical Surveys 3 Sbornik: Mathematics 3 Sibirskie Èlektronnye Matematicheskie Izvestiya 2 Mathematical Notes 2 Bulletin des Sciences Mathématiques 2 Izvestiya: Mathematics 2 Complex Variables and Elliptic Equations 2 Eurasian Mathematical Journal 1 Matematicheskie Zametki 1 Uspekhi Matematicheskikh Nauk [N. S.] 1 Annales de l’Institut Fourier 1 Mathematische Annalen 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Acta Applicandae Mathematicae 1 Mathematics of the USSR, Sbornik 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Matematicheskiĭ Sbornik 1 Russian Mathematics 1 Calculus of Variations and Partial Differential Equations 1 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 1 Contemporary Mathematics 1 Problemy Analiza. Issues of Analysis all top 5 Fields 89 Functions of a complex variable (30-XX) 81 Functional analysis (46-XX) 34 Potential theory (31-XX) 24 Topological groups, Lie groups (22-XX) 24 Differential geometry (53-XX) 23 Abstract harmonic analysis (43-XX) 14 Operator theory (47-XX) 13 Global analysis, analysis on manifolds (58-XX) 12 History and biography (01-XX) 11 Real functions (26-XX) 11 Partial differential equations (35-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 5 General and overarching topics; collections (00-XX) 5 Measure and integration (28-XX) 3 General topology (54-XX) 2 Convex and discrete geometry (52-XX) 2 Numerical analysis (65-XX) 2 Mechanics of deformable solids (74-XX) 1 Mathematical logic and foundations (03-XX) 1 Group theory and generalizations (20-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Geometry (51-XX) 1 Computer science (68-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 105 Publications have been cited 752 times in 287 Documents Cited by ▼ Year ▼ Geometry of Carnot-Carathéodory spaces and differentiability of mappings. Zbl 1146.53023Vodopyanov, S. K. 51 2007 Geometry of Carnot-Carathéodory spaces differentiability, coarea and area formulas. Zbl 1297.53029Karmanova, Maria; Vodop’yanov, Sergey 49 2009 Regularity of mappings inverse to Sobolev mappings. Zbl 1266.26019Vodop’yanov, S. K. 26 2012 Set functions and their applications in the theory of Lebesgue and Sobolev spaces. I. Zbl 1089.47027Vodop’yanov, S. K.; Ukhlov, A. D. 25 2004 Superposition operators in Sobolev spaces. Zbl 1033.47020Vodop’yanov, S. K.; Ukhlov, A. D. 22 2002 Approximate differentiability of mappings of Carnot-Carathéodory spaces. Zbl 1293.53041Basalaev, S. G.; Vodopyanov, S. K. 21 2013 Sobolev spaces and \((P,Q)\)-quasiconformal mappings of Carnot groups. Zbl 0917.46023Vodop’yanov, S. K.; Ukhlov, A. D. 20 1998 Monotone functions and quasiconformal mappings on Carnot groups. Zbl 0876.30020Vodop’yanov, S. K. 19 1996 \(\mathcal P\)-differentiability on Carnot groups in different topologies and related topics. Zbl 0992.58005Vodop’yanov, Serguei K. 19 2000 Quasiconformal mappings and spaces of functions with generalized first derivatives. Zbl 0353.30019Vodop’yanov, S. K.; Gol’dshtejn, V. M. 19 1977 Mappings associated with weighted Sobolev spaces. Zbl 1166.30012Ukhlov, A.; Vodopyanov, S. K. 18 2008 Mappings with bounded \((P,Q)\)-distortion on Carnot groups. Zbl 1213.30049Ukhlov, A.; Vodop’yanov, S. K. 17 2010 A classification of sub-Riemannian manifolds. Zbl 0937.31013Vodop’yanov, S. K.; Markina, I. G. 15 1998 On geometric properties of functions with generalized first derivatives. Zbl 0429.30017Vodop’yanov, S. K.; Gol’dshteĭn, V. M.; Reshetnyak, Yu. G. 14 1979 A coarea formula for smooth contact mappings of Carnot-Carathéodory spaces. Zbl 1304.53024Karmanova, M.; Vodopyanov, S. 14 2013 Liouville type theorems for mappings with bounded (co)-distortion. Zbl 1019.30022Troyanov, Marc; Vodop’yanov, Sergei 13 2002 Superposition operators in the Lebesgue spaces and differentiability of quasiadditive set functions. Zbl 1050.47031Vodopyanov, S. K.; Ukhlov, A. D. 13 2002 Lattice isomorphisms of the spaces \(W^1_n\) and quasiconformal mappings. Zbl 0324.46040Vodop’yanov, S. K.; Gol’dshtejn, V. M. 13 1975 Analytic properties of quasiconformal mappings on Carnot groups. Zbl 0891.30013Vodop’yanov, S. K.; Greshnov, A. V. 11 1995 Approximately differentiable transformations and change of variables on nilpotent groups. Zbl 0870.43005Vodop’yanov, S. K.; Ukhlov, A. D. 11 1996 Capacity estimates, Liouville’s theorem, and singularity removal for mappings with bounded \((p,q)\)-distortion. Zbl 1341.30016Baykin, A. N.; Vodop’yanov, S. K. 11 2015 Local geometry of Carnot manifolds under minimal smoothness. Zbl 1175.53046Vodop’yanov, S. K.; Karmanova, M. B. 11 2007 Isomorphisms of Sobolev spaces on Carnot groups and quasi-isometric mappings. Zbl 1322.46025Vodop’yanov, S. K.; Evseev, N. A. 10 2014 On extension of functions of bounded mean oscillation from domains in a space of homogeneous type with intrinsic metric. Zbl 0865.30029Vodop’yanov, S. K.; Greshnov, A. V. 9 1995 Criteria for extension of functions of the class \(L^1_2\) from unbounded plane domains. Zbl 0436.30013Vodop’yanov, S. K.; Gol’dshtejn, V. M.; Latfullin, T. G. 9 1979 Coercive estimates and integral representation formulas on Carnot groups. Zbl 1219.43007Isangulova, D. V.; Vodopyanov, S. K. 9 2010 On local approximation theorem on equiregular Carnot-Carathéodory spaces. Zbl 1294.53032Karmanova, Maria; Vodopyanov, Sergey 9 2014 On the regularity of the Poletskii function under weak analytic assumptions on the given mapping. Zbl 1305.26031Vodop’yanov, S. K. 8 2014 Set functions and their applications in the theory of Lebesgue and Sobolev spaces. I. Zbl 1050.47030Vodopyanov, S. K.; Ukhlov, A. D. 8 2003 Mappings of homogeneous groups and imbeddings of functional spaces. Zbl 0731.46019Vodop’yanov, S. K. 8 1989 Criteria for the removability of sets in spaces of \(L^1_p\) quasiconformal and quasi-isometric mappings. Zbl 0409.46032Vodop’yanov, S. K.; Gol’dshtejn, V. M. 8 1977 Prolongement de fonctions différentiables hors de domaines plans. Zbl 0482.46019Gol’dstein, Vladimir; Vodop’janov, Serge 8 1981 A local approximation theorem on Carnot manifolds under minimal smoothness conditions. Zbl 1188.53029Vodop’yanov, S. K.; Karmanova, M. V. 8 2009 Topological and geometrical properties of mappings with summable Jacobian in Sobolev classes. I. Zbl 0983.30009Vodop’yanov, S. K. 7 2000 Spaces of differential forms and maps with controlled distortion. Zbl 1203.46025Vodop’yanov, S. K. 7 2010 An area formula for \(C^{1}\)-smooth contact mappings of Carnot manifolds. Zbl 1180.53035Vodop’yanov, S. K.; Karmanova, M. B. 7 2008 Sub-Riemannian geometry for vector fields of minimal smoothness. Zbl 1184.53035Vodop’yanov, S. K.; Karmanova, M. B. 7 2008 Superposition operators in Sobolev spaces. Zbl 1246.30044Vodop’yanov, S. K.; Ukhlov, A. D. 7 2002 On regularity of mappings inverse to Sobolev mappings. Zbl 1234.30023Vodop’yanov, S. K. 7 2008 Taylor’s formula and function spaces. Textbook. (Формула Тейлора и функционалъные пространства. Учебное пособие.) Zbl 0709.46009Vodop’yanov, S. K. 6 1988 Composition operators on Sobolev spaces. Zbl 1098.46027Vodopyanov, S. K. 6 2005 Foundations of the theory of mappings with bounded distortion on Carnot groups. Zbl 1146.53045Vodopyanov, S. K. 6 2007 An area formula for contact \(C^{1}\)-mappings of Carnot manifolds. Zbl 1193.51015Karmanova, Maria; Vodopyanov, Sergey 6 2010 A coarea formula for smooth contact mappings of Carnot manifolds. Zbl 1153.53056Vodop’yanov, S. K.; Karmanova, M. B. 6 2007 On the differentiability of mappings of Carnot-Carathéodory spaces. Zbl 1246.30043Vodop’yanov, S. K.; Greshnov, A. V. 6 2003 Functional characteristics of quasiisometric mappings. Zbl 0389.30014Vodop’yanov, S. K.; Gol’dshtejn, V. M. 6 1977 Differentiability of curves in the category of Carnot manifolds. Zbl 1134.53017Vodop’yanov, S. K. 6 2006 Sharp geometric rigidity of isometries on Heisenberg groups. Zbl 1279.53030Isangulova, D. V.; Vodopyanov, S. K. 6 2013 Differentiability of mappings of the Sobolev space \(W_{n-1}^1\) with conditions on the distortion function. Zbl 1412.30094Vodopyanov, S. K. 6 2018 Basics of the quasiconformal analysis of a two-index scale of spatial mappings. Zbl 1415.30022Vodopyanov, S. K. 6 2018 Mappings with bounded distortion and with finite distortion on Carnot groups. Zbl 0973.30021Vodop’yanov, S. K. 5 1998 Potential theory on homogeneous groups. Zbl 0673.31005Vodop’yanov, S. K. 5 1989 On value distributions for quasimeromorphic mappings on \(\mathbb H\)-type Carnot groups. Zbl 1110.32006Markina, Irina; Vodopyanov, Sergey 5 2006 Isomorphisms of Sobolev spaces on Carnot groups and metric properties of mappings. Zbl 1348.46044Vodop’yanov, S. K.; Evseev, N. A. 4 2015 Local estimates of the variation of mappings with bounded \(s\)-distortion on Carnot groups. Zbl 0962.30007Vodop’yanov, S. K.; Markina, I. G. 4 1999 Weighted \(L_ p\)-potential theory on homogeneous groups. Zbl 0787.31012Vodop’yanov, S. K. 4 1992 Closure of classes of mappings with bounded distortion on Carnot groups. Zbl 1076.30025Vodop’yanov, S. K. 4 2004 Whitney-type theorems on extension of functions on Carnot groups. Zbl 1155.30346Vodopyanov, S. K.; Pupyshev, I. M. 4 2006 Injectivity almost everywhere and mappings with finite distortion in nonlinear elasticity. Zbl 1430.30011Molchanova, Anastasia; Vodopyanov, Sergey 4 2020 Admissible changes of variables for Sobolev functions on (sub-)Riemannian manifolds. Zbl 1422.58002Vodopyanov, S. K. 4 2019 Isomorphisms of Sobolev spaces on Carnot groups and quasiconformal mappings. Zbl 1348.46045Vodop’yanov, S. K.; Evseev, N. A. 3 2015 Variational problems of nonlinear elasticity in certain classes of mappings with finite distortion. Zbl 1336.49017Vodop’yanov, S. K.; Molchanova, A. O. 3 2015 The interaction of analysis and geometry. International school-conference on analysis and geometry, Novosibirsk, Russia, August 23–September 3, 2004. Zbl 1109.00005 3 2007 Mappings of finite codistortion and Sobolev classes of functions. Zbl 1242.26012Vodopyanov, S. K. 3 2011 Isomorphisms of Sobolev spaces on Riemannian manifolds and quasiconformal mappings. Zbl 1444.46029Vodopyanov, S. K. 3 2019 On admissible changes of variables for Sobolev functions on (sub)Riemannian manifolds. Zbl 1365.46030Vodopyanov, S. K. 3 2016 On closedness of classes of mappings with bounded distortion on Carnot groups. Zbl 1015.30008Vodop’yanov, S. K. 2 2002 Weighted Sobolev spaces and boundary behavior of solutions to degenerate hypoelliptic equations. Zbl 0878.46024Vodop’yanov, S. K. 2 1995 Sobolev spaces and hypoelliptic equations. Zbl 0925.46011Vodop’yanov, S. K.; Chernikov, V. M. 2 1995 Normal families of mappings on Carnot groups. Zbl 0876.30021Vodop’yanov, S. K.; Kudryavtseva, N. A. 2 1996 Differentiability of mappings of Carnot manifolds and isomorphism of tangent cones. Zbl 1206.53037Vodop’yanov, S. K. 2 2006 Selected works. Vol. II. Functional analysis. Partial differential equations. Compiled and edited by S. K. Vodop’yanov and G. V. Demidenko. (Избранные труды. Том II. Функциональный анализ. Дифференциальные уравнения с частными производными.) Zbl 1325.01034Sobolev, S. L. 2 2006 Weighted Sobolev spaces and quasiconformal mappings. Zbl 1127.46023Vodop’yanov, S. K.; Ukhlov, A. D. 2 2005 Differentiability of the mappings of Carnot-Carathéodory spaces in the Sobolev and \(BV\)-topologies. Zbl 1164.46327Vodop’yanov, S. K.; Isangulova, D. V. 2 2007 Differentiability of mappings in the geometry of Carnot manifolds. Zbl 1164.53345Vodop’yanov, S. K. 2 2007 Set functions and their applications in the theory of Lebesgue and Sobolev spaces. II. Zbl 1091.47027Vodop’yanov, S. K.; Ukhlov, A. D. 2 2005 Potential theory on homogeneous groups. Zbl 0695.31009Vodop’yanov, S. K. 2 1990 The regularity of inverses to Sobolev mappings and the theory of \(\mathcal{Q}_{q,p} \)-homeomorphisms. Zbl 1456.30046Vodopyanov, S. K. 2 2020 On the convergence of mappings with \(k\)-finite distortion. Zbl 1393.30020Vodop’yanov, S. K.; Kudryavtseva, N. A. 2 2017 Sobolev \(W^1_p\)-spaces on \(d\)-thick closed subsets of \({\mathbb{R}}^n \). Zbl 1462.46044Vodopyanov, S. K.; Tyulenev, A. I. 2 2020 On grand Sobolev spaces and pointwise description of Banach function spaces. Zbl 1464.46031Jain, Pankaj; Molchanova, Anastasia; Singh, Monika; Vodopyanov, Sergey 2 2021 Lower semicontinuity of mappings with bounded \((\theta, 1)\)-weighted \((p,q)\)-distortion. Zbl 1359.30040Vodop’yanov, S. K.; Molchanova, A. O. 2 2016 On the Whitney problem for weighted Sobolev spaces. Zbl 06731613Tyulenev, A. I.; Vodop’yanov, S. K. 2 2017 Composition operators on weighted Sobolev spaces and the theory of \(\mathcal{Q}_p\)-homeomorphisms. Zbl 1477.30053Vodopyanov, S. K. 2 2020 Exceptional sets for solutions to subelliptic equations. Zbl 0858.35026Vodop’yanov, S. K.; Markina, I. G. 1 1995 Topological properties of mappings from the Sobolev classes with summable Jacobian. Zbl 0961.46019Vodop’yanov, S. K. 1 1998 Estimates of the deviation from a sphere of quasiumbilical surfaces. Zbl 0214.49205Vodop’yanov, S. K. 1 1971 Geometric properties of domains and mappings. Lower estimates for the norm of the extension operator. Zbl 0634.46024Vodop’yanov, S. K. 1 1987 The maximum principle in potential theory and imbedding theorems for anisotropic spaces of differentiable functions. Zbl 0646.31010Vodop’yanov, S. K. 1 1988 On removable singularities of bounded solutions to quasielliptic equations. Zbl 0791.35023Alborova, M. S.; Vodop’yanov, S. K. 1 1992 Maximum principle in potential theory and imbedding theorems for anisotropic spaces of differentiable functions. Zbl 0699.31019Vodop’yanov, S. K. 1 1988 L\({}_ p\)-potential theory for generalized kernels. Zbl 0716.31003Vodop’yanov, S. K. 1 1990 On the closedness of classes of mappings with bounded distortion on Carnot groups. Zbl 1064.30013Vodop’yanov, S. K. 1 2001 Geometry of Carnot-Carathéodory spaces, quasiconformal analysis, and geometric measure theory. Zbl 1048.43011Vodopyanov, S. K. 1 2003 Weighted \(L_ p\)-potential theory on homogeneous groups. Zbl 0774.31009Vodop’yanov, S. K. 1 1992 Algebraic properties of the tangent cone to a quasimetric space with dilations. Zbl 1198.53033Vodop’yanov, S. K.; Selivanova, S. V. 1 2009 Foundations of the theory of mappings with bounded distortion on Carnot groups. Zbl 1219.30010Vodop’yanov, S. K. 1 2005 Intrinsic geometries and boundary values of differentiable functions. I. Zbl 0692.46025Vodop’yanov, S. K. 1 1989 A criterion for the possibility of eliminating sets for the spaces \(W^1_p\) of quasiconformal and quasi-isometric mappings. Zbl 0321.30024Vodop’yanov, S. K.; Gol’dshtejn, V. M. 1 1975 Functional characteristics of quasi-isometric mappings. Zbl 0364.30030Vodop’yanov, S. K.; Gol’dshtejn, V. M. 1 1976 On grand Sobolev spaces and pointwise description of Banach function spaces. Zbl 1464.46031Jain, Pankaj; Molchanova, Anastasia; Singh, Monika; Vodopyanov, Sergey 2 2021 Moduli inequalities for \(W^1_{n-1,\mathrm{loc}}\)-mappings with weighted bounded \((q, p)\)-distortion. Zbl 1469.30050Vodopyanov, S. K. 1 2021 Functional and analytic properties of a class of mappings in quasi-conformal analysis. Zbl 07485056Vodopyanov, S. K.; Tomilov, A. O. 1 2021 Injectivity almost everywhere and mappings with finite distortion in nonlinear elasticity. Zbl 1430.30011Molchanova, Anastasia; Vodopyanov, Sergey 4 2020 The regularity of inverses to Sobolev mappings and the theory of \(\mathcal{Q}_{q,p} \)-homeomorphisms. Zbl 1456.30046Vodopyanov, S. K. 2 2020 Sobolev \(W^1_p\)-spaces on \(d\)-thick closed subsets of \({\mathbb{R}}^n \). Zbl 1462.46044Vodopyanov, S. K.; Tyulenev, A. I. 2 2020 Composition operators on weighted Sobolev spaces and the theory of \(\mathcal{Q}_p\)-homeomorphisms. Zbl 1477.30053Vodopyanov, S. K. 2 2020 Admissible changes of variables for Sobolev functions on (sub-)Riemannian manifolds. Zbl 1422.58002Vodopyanov, S. K. 4 2019 Isomorphisms of Sobolev spaces on Riemannian manifolds and quasiconformal mappings. Zbl 1444.46029Vodopyanov, S. K. 3 2019 Foundations of quasiconformal analysis of a two-index scale of spatial mappings. Zbl 1418.30015Vodopyanov, S. K. 1 2019 Differentiability of mappings of the Sobolev space \(W_{n-1}^1\) with conditions on the distortion function. Zbl 1412.30094Vodopyanov, S. K. 6 2018 Basics of the quasiconformal analysis of a two-index scale of spatial mappings. Zbl 1415.30022Vodopyanov, S. K. 6 2018 On the convergence of mappings with \(k\)-finite distortion. Zbl 1393.30020Vodop’yanov, S. K.; Kudryavtseva, N. A. 2 2017 On the Whitney problem for weighted Sobolev spaces. Zbl 06731613Tyulenev, A. I.; Vodop’yanov, S. K. 2 2017 On admissible changes of variables for Sobolev functions on (sub)Riemannian manifolds. Zbl 1365.46030Vodopyanov, S. K. 3 2016 Lower semicontinuity of mappings with bounded \((\theta, 1)\)-weighted \((p,q)\)-distortion. Zbl 1359.30040Vodop’yanov, S. K.; Molchanova, A. O. 2 2016 Capacity estimates, Liouville’s theorem, and singularity removal for mappings with bounded \((p,q)\)-distortion. Zbl 1341.30016Baykin, A. N.; Vodop’yanov, S. K. 11 2015 Isomorphisms of Sobolev spaces on Carnot groups and metric properties of mappings. Zbl 1348.46044Vodop’yanov, S. K.; Evseev, N. A. 4 2015 Isomorphisms of Sobolev spaces on Carnot groups and quasiconformal mappings. Zbl 1348.46045Vodop’yanov, S. K.; Evseev, N. A. 3 2015 Variational problems of nonlinear elasticity in certain classes of mappings with finite distortion. Zbl 1336.49017Vodop’yanov, S. K.; Molchanova, A. O. 3 2015 Isomorphisms of Sobolev spaces on Carnot groups and quasi-isometric mappings. Zbl 1322.46025Vodop’yanov, S. K.; Evseev, N. A. 10 2014 On local approximation theorem on equiregular Carnot-Carathéodory spaces. Zbl 1294.53032Karmanova, Maria; Vodopyanov, Sergey 9 2014 On the regularity of the Poletskii function under weak analytic assumptions on the given mapping. Zbl 1305.26031Vodop’yanov, S. K. 8 2014 Approximate differentiability of mappings of Carnot-Carathéodory spaces. Zbl 1293.53041Basalaev, S. G.; Vodopyanov, S. K. 21 2013 A coarea formula for smooth contact mappings of Carnot-Carathéodory spaces. Zbl 1304.53024Karmanova, M.; Vodopyanov, S. 14 2013 Sharp geometric rigidity of isometries on Heisenberg groups. Zbl 1279.53030Isangulova, D. V.; Vodopyanov, S. K. 6 2013 Regularity of mappings inverse to Sobolev mappings. Zbl 1266.26019Vodop’yanov, S. K. 26 2012 Mappings of finite codistortion and Sobolev classes of functions. Zbl 1242.26012Vodopyanov, S. K. 3 2011 Mappings with bounded \((P,Q)\)-distortion on Carnot groups. Zbl 1213.30049Ukhlov, A.; Vodop’yanov, S. K. 17 2010 Coercive estimates and integral representation formulas on Carnot groups. Zbl 1219.43007Isangulova, D. V.; Vodopyanov, S. K. 9 2010 Spaces of differential forms and maps with controlled distortion. Zbl 1203.46025Vodop’yanov, S. K. 7 2010 An area formula for contact \(C^{1}\)-mappings of Carnot manifolds. Zbl 1193.51015Karmanova, Maria; Vodopyanov, Sergey 6 2010 Geometry of Carnot-Carathéodory spaces differentiability, coarea and area formulas. Zbl 1297.53029Karmanova, Maria; Vodop’yanov, Sergey 49 2009 A local approximation theorem on Carnot manifolds under minimal smoothness conditions. Zbl 1188.53029Vodop’yanov, S. K.; Karmanova, M. V. 8 2009 Algebraic properties of the tangent cone to a quasimetric space with dilations. Zbl 1198.53033Vodop’yanov, S. K.; Selivanova, S. V. 1 2009 Nonlinear potential theory for Sobolev spaces on Carnot groups. Zbl 1224.46070Vodop’yanov, S. K.; Kudryavtseva, N. A. 1 2009 Mappings associated with weighted Sobolev spaces. Zbl 1166.30012Ukhlov, A.; Vodopyanov, S. K. 18 2008 An area formula for \(C^{1}\)-smooth contact mappings of Carnot manifolds. Zbl 1180.53035Vodop’yanov, S. K.; Karmanova, M. B. 7 2008 Sub-Riemannian geometry for vector fields of minimal smoothness. Zbl 1184.53035Vodop’yanov, S. K.; Karmanova, M. B. 7 2008 On regularity of mappings inverse to Sobolev mappings. Zbl 1234.30023Vodop’yanov, S. K. 7 2008 Sharp bounds for geometric rigidity of isometries on Heisenberg groups. Zbl 1160.43005Vodop’yanov, S. K.; Isangulova, D. V. 1 2008 Geometry of Carnot-Carathéodory spaces and differentiability of mappings. Zbl 1146.53023Vodopyanov, S. K. 51 2007 Local geometry of Carnot manifolds under minimal smoothness. Zbl 1175.53046Vodop’yanov, S. K.; Karmanova, M. B. 11 2007 Foundations of the theory of mappings with bounded distortion on Carnot groups. Zbl 1146.53045Vodopyanov, S. K. 6 2007 A coarea formula for smooth contact mappings of Carnot manifolds. Zbl 1153.53056Vodop’yanov, S. K.; Karmanova, M. B. 6 2007 The interaction of analysis and geometry. International school-conference on analysis and geometry, Novosibirsk, Russia, August 23–September 3, 2004. Zbl 1109.00005 3 2007 Differentiability of the mappings of Carnot-Carathéodory spaces in the Sobolev and \(BV\)-topologies. Zbl 1164.46327Vodop’yanov, S. K.; Isangulova, D. V. 2 2007 Differentiability of mappings in the geometry of Carnot manifolds. Zbl 1164.53345Vodop’yanov, S. K. 2 2007 Differentiability of curves in the category of Carnot manifolds. Zbl 1134.53017Vodop’yanov, S. K. 6 2006 On value distributions for quasimeromorphic mappings on \(\mathbb H\)-type Carnot groups. Zbl 1110.32006Markina, Irina; Vodopyanov, Sergey 5 2006 Whitney-type theorems on extension of functions on Carnot groups. Zbl 1155.30346Vodopyanov, S. K.; Pupyshev, I. M. 4 2006 Differentiability of mappings of Carnot manifolds and isomorphism of tangent cones. Zbl 1206.53037Vodop’yanov, S. K. 2 2006 Selected works. Vol. II. Functional analysis. Partial differential equations. Compiled and edited by S. K. Vodop’yanov and G. V. Demidenko. (Избранные труды. Том II. Функциональный анализ. Дифференциальные уравнения с частными производными.) Zbl 1325.01034Sobolev, S. L. 2 2006 Composition operators on Sobolev spaces. Zbl 1098.46027Vodopyanov, S. K. 6 2005 Weighted Sobolev spaces and quasiconformal mappings. Zbl 1127.46023Vodop’yanov, S. K.; Ukhlov, A. D. 2 2005 Set functions and their applications in the theory of Lebesgue and Sobolev spaces. II. Zbl 1091.47027Vodop’yanov, S. K.; Ukhlov, A. D. 2 2005 Foundations of the theory of mappings with bounded distortion on Carnot groups. Zbl 1219.30010Vodop’yanov, S. K. 1 2005 Set functions and their applications in the theory of Lebesgue and Sobolev spaces. I. Zbl 1089.47027Vodop’yanov, S. K.; Ukhlov, A. D. 25 2004 Closure of classes of mappings with bounded distortion on Carnot groups. Zbl 1076.30025Vodop’yanov, S. K. 4 2004 Set functions and their applications in the theory of Lebesgue and Sobolev spaces. I. Zbl 1050.47030Vodopyanov, S. K.; Ukhlov, A. D. 8 2003 On the differentiability of mappings of Carnot-Carathéodory spaces. Zbl 1246.30043Vodop’yanov, S. K.; Greshnov, A. V. 6 2003 Geometry of Carnot-Carathéodory spaces, quasiconformal analysis, and geometric measure theory. Zbl 1048.43011Vodopyanov, S. K. 1 2003 Superposition operators in Sobolev spaces. Zbl 1033.47020Vodop’yanov, S. K.; Ukhlov, A. D. 22 2002 Liouville type theorems for mappings with bounded (co)-distortion. Zbl 1019.30022Troyanov, Marc; Vodop’yanov, Sergei 13 2002 Superposition operators in the Lebesgue spaces and differentiability of quasiadditive set functions. Zbl 1050.47031Vodopyanov, S. K.; Ukhlov, A. D. 13 2002 Superposition operators in Sobolev spaces. Zbl 1246.30044Vodop’yanov, S. K.; Ukhlov, A. D. 7 2002 On closedness of classes of mappings with bounded distortion on Carnot groups. Zbl 1015.30008Vodop’yanov, S. K. 2 2002 On the closedness of classes of mappings with bounded distortion on Carnot groups. Zbl 1064.30013Vodop’yanov, S. K. 1 2001 \(\mathcal P\)-differentiability on Carnot groups in different topologies and related topics. Zbl 0992.58005Vodop’yanov, Serguei K. 19 2000 Topological and geometrical properties of mappings with summable Jacobian in Sobolev classes. I. Zbl 0983.30009Vodop’yanov, S. K. 7 2000 Local estimates of the variation of mappings with bounded \(s\)-distortion on Carnot groups. Zbl 0962.30007Vodop’yanov, S. K.; Markina, I. G. 4 1999 Sobolev spaces and \((P,Q)\)-quasiconformal mappings of Carnot groups. Zbl 0917.46023Vodop’yanov, S. K.; Ukhlov, A. D. 20 1998 A classification of sub-Riemannian manifolds. Zbl 0937.31013Vodop’yanov, S. K.; Markina, I. G. 15 1998 Mappings with bounded distortion and with finite distortion on Carnot groups. Zbl 0973.30021Vodop’yanov, S. K. 5 1998 Topological properties of mappings from the Sobolev classes with summable Jacobian. Zbl 0961.46019Vodop’yanov, S. K. 1 1998 Monotone functions and quasiconformal mappings on Carnot groups. Zbl 0876.30020Vodop’yanov, S. K. 19 1996 Approximately differentiable transformations and change of variables on nilpotent groups. Zbl 0870.43005Vodop’yanov, S. K.; Ukhlov, A. D. 11 1996 Normal families of mappings on Carnot groups. Zbl 0876.30021Vodop’yanov, S. K.; Kudryavtseva, N. A. 2 1996 Analytic properties of quasiconformal mappings on Carnot groups. Zbl 0891.30013Vodop’yanov, S. K.; Greshnov, A. V. 11 1995 On extension of functions of bounded mean oscillation from domains in a space of homogeneous type with intrinsic metric. Zbl 0865.30029Vodop’yanov, S. K.; Greshnov, A. V. 9 1995 Weighted Sobolev spaces and boundary behavior of solutions to degenerate hypoelliptic equations. Zbl 0878.46024Vodop’yanov, S. K. 2 1995 Sobolev spaces and hypoelliptic equations. Zbl 0925.46011Vodop’yanov, S. K.; Chernikov, V. M. 2 1995 Exceptional sets for solutions to subelliptic equations. Zbl 0858.35026Vodop’yanov, S. K.; Markina, I. G. 1 1995 Weighted \(L_ p\)-potential theory on homogeneous groups. Zbl 0787.31012Vodop’yanov, S. K. 4 1992 On removable singularities of bounded solutions to quasielliptic equations. Zbl 0791.35023Alborova, M. S.; Vodop’yanov, S. K. 1 1992 Weighted \(L_ p\)-potential theory on homogeneous groups. Zbl 0774.31009Vodop’yanov, S. K. 1 1992 Potential theory on homogeneous groups. Zbl 0695.31009Vodop’yanov, S. K. 2 1990 L\({}_ p\)-potential theory for generalized kernels. Zbl 0716.31003Vodop’yanov, S. K. 1 1990 Mappings of homogeneous groups and imbeddings of functional spaces. Zbl 0731.46019Vodop’yanov, S. K. 8 1989 Potential theory on homogeneous groups. Zbl 0673.31005Vodop’yanov, S. K. 5 1989 Intrinsic geometries and boundary values of differentiable functions. I. Zbl 0692.46025Vodop’yanov, S. K. 1 1989 Taylor’s formula and function spaces. Textbook. (Формула Тейлора и функционалъные пространства. Учебное пособие.) Zbl 0709.46009Vodop’yanov, S. K. 6 1988 The maximum principle in potential theory and imbedding theorems for anisotropic spaces of differentiable functions. Zbl 0646.31010Vodop’yanov, S. K. 1 1988 Maximum principle in potential theory and imbedding theorems for anisotropic spaces of differentiable functions. Zbl 0699.31019Vodop’yanov, S. K. 1 1988 Geometric properties of domains and mappings. Lower estimates for the norm of the extension operator. Zbl 0634.46024Vodop’yanov, S. K. 1 1987 Prolongement de fonctions différentiables hors de domaines plans. Zbl 0482.46019Gol’dstein, Vladimir; Vodop’janov, Serge 8 1981 On geometric properties of functions with generalized first derivatives. Zbl 0429.30017Vodop’yanov, S. K.; Gol’dshteĭn, V. M.; Reshetnyak, Yu. G. 14 1979 Criteria for extension of functions of the class \(L^1_2\) from unbounded plane domains. Zbl 0436.30013Vodop’yanov, S. K.; Gol’dshtejn, V. M.; Latfullin, T. G. 9 1979 Quasiconformal mappings and spaces of functions with generalized first derivatives. Zbl 0353.30019Vodop’yanov, S. K.; Gol’dshtejn, V. M. 19 1977 Criteria for the removability of sets in spaces of \(L^1_p\) quasiconformal and quasi-isometric mappings. Zbl 0409.46032Vodop’yanov, S. K.; Gol’dshtejn, V. M. 8 1977 ...and 5 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 184 Authors 56 Karmanova, Maria B. 47 Vodop’yanov, Sergeĭ Konstantinovich 23 Ukhlov, Alexander Dadar-Oolovich 20 Gol’dshtein, Vladimir Mikhailovich 11 Evseev, Nikita Aleksandrovich 9 Ryazanov, Vladimir Il’ich 9 Sevost’yanov, Yevgen Oleksandrovych 7 Isangulova, D. V. 7 Salimov, Ruslan Radikovich 6 Greshnov, Aleksandr Valer’evich 6 Markina, Irina 6 Molchanova, Anastasia Olegovna 6 Selivanova, Svetlana V. 6 Tryamkin, Maksim Vladimirovich 5 Basalaev, S. G. 5 Morbidelli, Daniele 5 Pchelintsev, Valerii 4 Gutlyanskiĭ, Vladimir Ya. 4 Koskela, Pekka 4 Menovshchikov, A. V. 4 Tyulenev, Alexander I. 3 Dymchenko, Yuriĭ Viktorovich 3 Garofalo, Nicola 3 Menovschikov, Alexander 3 Monti, Roberto 3 Müller, Stefan 3 Troyanov, Marc 3 Zhou, Yuan 3 Zobin, Nahum 2 Battaglia, Erika 2 Buckley, Stephen M. 2 Capogna, Luca 2 Fässler, Katrin S. 2 Franchi, Bruno 2 Heinonen, Juha 2 Henao, Duvan A. 2 Hurri-Syrjānen, Ritva 2 Kleprlík, Luděk 2 Kovtonyuk, D. A. 2 Kudryavtseva, N. A. 2 Lomako, Tetiana 2 Montanari, Annamaria 2 Montefalcone, Francescopaolo 2 Nhieu, Duy-Minh 2 Pchelintsev, V. A. 2 Peltonen, Kirsi 2 Serra Cassano, Francesco 2 Shvartsman, Pavel 2 Spector, Scott J. 1 Adamowicz, Tomasz 1 Alborova, M. S. 1 Ambrosio, Luigi 1 Arutyunov, Aram Vladimirovic 1 Ball, John MacLeod 1 Balogh, Zoltán M. 1 Barchiesi, Marco 1 Baykin, Alekseĭ N. 1 Bei, Francesco 1 Biagi, Stefano 1 Biegert, Markus 1 Biroli, Marco 1 Björn, Anders 1 Bojarski, Bogdan 1 Bonfiglioli, Andrea 1 Bouali, Bouchta 1 Brakalova, Melkana Aleksandrova 1 Bramanti, Marco 1 Brandolini, Luca 1 Brewster, Kevin 1 Bukhvalov, Alexander V. 1 Buliga, Marius G. 1 Charifi, Ahmed 1 Chebanenko, Nikita Alekseevich 1 Christ, Michael 1 Ciarlet, Philippe Gaston 1 Cinti, Eleonora 1 Citti, Giovanna 1 Cowling, Michael G. 1 Danielli, Donatella 1 Davoli, Elisa 1 De Cicco, Virginia 1 Egorov, Aleksandr Anatol’evich 1 Farroni, Fernando 1 Filatov, Vladimir Vladimirovich 1 Fiorenza, Alberto 1 Friesecke, Gero 1 Gaczkowski, Michał 1 Gamara, Najoua 1 Giova, Raffaella 1 González, María del Mar 1 Górka, Przemysław 1 Guerra, André 1 Güneysu, Batu 1 Gurov, L. G. 1 Hashash, Paz 1 Hencl, Stanislav 1 Herron, David A. 1 Huang, Yonghong 1 Jain, Pankaj 1 James, Richard D. ...and 84 more Authors all top 5 Cited in 78 Serials 61 Siberian Mathematical Journal 47 Doklady Mathematics 15 Journal of Mathematical Sciences (New York) 10 Journal of Mathematical Analysis and Applications 9 Mathematical Notes 7 Archive for Rational Mechanics and Analysis 7 The Journal of Geometric Analysis 6 Journal of Functional Analysis 6 Russian Mathematics 5 Journal d’Analyse Mathématique 5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 Calculus of Variations and Partial Differential Equations 5 St. Petersburg Mathematical Journal 4 Complex Variables and Elliptic Equations 3 Advances in Mathematics 3 Mathematische Zeitschrift 3 Transactions of the American Mathematical Society 3 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 3 Potential Analysis 3 Bulletin des Sciences Mathématiques 3 Vladikavkazskiĭ Matematicheskiĭ Zhurnal 3 Complex Analysis and Operator Theory 2 Israel Journal of Mathematics 2 Arkiv för Matematik 2 Acta Mathematica 2 Journal of Soviet Mathematics 2 Mathematische Nachrichten 2 Proceedings of the American Mathematical Society 2 Geometric and Functional Analysis. GAFA 2 Georgian Mathematical Journal 2 Izvestiya: Mathematics 2 Lobachevskii Journal of Mathematics 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 2 Sibirskie Èlektronnye Matematicheskie Izvestiya 2 Analysis and Mathematical Physics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Ukrainian Mathematical Journal 1 Annales de l’Institut Fourier 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Duke Mathematical Journal 1 Illinois Journal of Mathematics 1 Integral Equations and Operator Theory 1 Journal of Differential Equations 1 Mathematische Annalen 1 Memoirs of the American Mathematical Society 1 Real Analysis Exchange 1 Results in Mathematics 1 Tohoku Mathematical Journal. Second Series 1 Acta Mathematica Hungarica 1 Acta Applicandae Mathematicae 1 Annals of Global Analysis and Geometry 1 Journal of Elasticity 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 SIAM Journal on Mathematical Analysis 1 Journal of Mathematical Imaging and Vision 1 Sbornik: Mathematics 1 The Journal of Fourier Analysis and Applications 1 Annales Academiae Scientiarum Fennicae. Mathematica 1 Matematicheskie Trudy 1 Journal of Dynamical and Control Systems 1 Communications in Contemporary Mathematics 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Seriya: Matematika, Mekhanika, Informatika 1 Computational Methods and Function Theory 1 Communications in Mathematical Analysis 1 Frontiers of Mathematics in China 1 Tbilisi Mathematical Journal 1 Science China. Mathematics 1 Izvestiya Saratovskogo Universiteta. Novaya Seriya. Seriya Matematika, Mekhanika, Informatika 1 Problemy Analiza. Issues of Analysis 1 Analysis and Geometry in Metric Spaces 1 Nonlinear Analysis. Theory, Methods & Applications 1 Transactions of A. Razmadze Mathematical Institute 1 Bollettino dell’Unione Matematica Italiana 1 Constructive Mathematical Analysis 1 Annales Fennici Mathematici all top 5 Cited in 32 Fields 97 Functions of a complex variable (30-XX) 93 Differential geometry (53-XX) 89 Functional analysis (46-XX) 49 Partial differential equations (35-XX) 31 Calculus of variations and optimal control; optimization (49-XX) 21 Operator theory (47-XX) 21 Global analysis, analysis on manifolds (58-XX) 20 Real functions (26-XX) 18 Topological groups, Lie groups (22-XX) 16 Abstract harmonic analysis (43-XX) 14 Potential theory (31-XX) 13 Mechanics of deformable solids (74-XX) 11 Measure and integration (28-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 7 General topology (54-XX) 5 Geometry (51-XX) 3 Combinatorics (05-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Manifolds and cell complexes (57-XX) 2 Nonassociative rings and algebras (17-XX) 2 Convex and discrete geometry (52-XX) 2 Numerical analysis (65-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Algebraic topology (55-XX) 1 Computer science (68-XX) 1 Optics, electromagnetic theory (78-XX) 1 Quantum theory (81-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year