Edit Profile (opens in new tab) Vodop’yanov, Sergeĭ Konstantinovich Co-Author Distance Author ID: vodopyanov.serguei-k Published as: Vodop’yanov, S. K.; Vodopyanov, S. K.; Vodopyanov, Sergey; Vodopyanov, Sergey K.; Vodop’janov, S. K.; Vodop’janov, Sergei Konstantinovitch; Vodop’yanov, Serguei K.; Vodop’yanov, Sergej K.; Vodopyanov, Sergei K.; Vodop’yanov, Serguei; Vodop’yanov, Sergei; Vodop’yanov, Sergey; Vodop’janov, Serge; Vodopjanov, S. K.; Vodopyanov, S. more...less External Links: MGP · ORCID · Math-Net.Ru Documents Indexed: 173 Publications since 1970, including 1 Book 6 Contributions as Editor Co-Authors: 128 Co-Authors with 106 Joint Publications 2,652 Co-Co-Authors all top 5 Co-Authors 70 single-authored 14 Gol’dshtejn, Vladimir M. 12 Ukhlov, Alexander Dadar-Oolovich 11 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 Kusraev, Anatoly Georgievich 4 Latfullin, T. G. 4 Molchanova, Anastasia Olegovna 3 Gutman, Aleksandr Efimovich 3 Vesnin, Andrei Yu. 2 Abanin, Aleksandr Vasil’evich 2 Basalaev, Sergey G. 2 Bokut, Leonid A. 2 Burenkov, Viktor Ivanovich 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 Umarkhadzhiev, Salaudin Musaevich 2 Valiev, Mars K. 1 Alborova, M. S. 1 Alexandrov, Victor A. 1 Arkhangel’skiĭ, Dmitriĭ A. 1 Avkhadiev, Farit Gabidinovich 1 Avsyankin, Oleg Gennadievich 1 Baizhanov, Bektur Sembiuly 1 Basaeva, Elena K. 1 Baykin, Alekseĭ N. 1 Belegradek, Oleg V. 1 Belyaev, V. Ya. 1 Beresmovskiĭ, V. N. 1 Borisenko, Aleksandr Andreevich 1 Botvinnik, V. A. 1 Boyarskij, Yu. I. 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 Erusalimskii, Yakov M. 1 Gitik, Moti 1 Gol’dman, Mikhail L’vovich 1 Gol’dshteyn, V. M. 1 Gol’dstein, Vladimir Mikailovitch 1 Goryainov, Viktor V. 1 Grigor’yan, Alexander Asaturovich 1 Guliyev, Vagif Sabir 1 Gurevich, Yuri 1 Iwaniec, Tadeusz 1 Jain, Pankaj 1 Karapetyants, Alekseĭ Nikolaevich 1 Karmanova, M. V. 1 Karyakin, Mikhail I. 1 Kesel’man, V. M. 1 Khudalov, Marat Zakharovich 1 Klimentov, Sergeĭ Borisovich 1 Klyachin, Vladimir Aleksandrovich 1 Koĭbaev, Vladimir Amurkhanovich 1 Kokilashvili, Vakhtang Mikhailovich 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 Liflyand, Elijah 1 Loboda, Aleksandr 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 Pskhu, Arsen Vladimirovich 1 Rabinovich, Vladimir Samuilovich 1 Rebrov, A. K. 1 Rodionov, Evgeniĭ Dmitrievich 1 Rogosin, Sergei V. ...and 29 more Co-Authors all top 5 Serials 38 Doklady Mathematics 35 Siberian Mathematical Journal 17 Sibirskiĭ Matematicheskiĭ Zhurnal 10 Vladikavkazskiĭ Matematicheskiĭ Zhurnal 8 Soviet Mathematics. Doklady 5 Matematicheskie Trudy 4 Siberian Advances in Mathematics 4 Sbornik: Mathematics 3 Russian Mathematical Surveys 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 92 Functions of a complex variable (30-XX) 84 Functional analysis (46-XX) 34 Potential theory (31-XX) 24 Topological groups, Lie groups (22-XX) 24 Abstract harmonic analysis (43-XX) 24 Differential geometry (53-XX) 14 Operator theory (47-XX) 13 History and biography (01-XX) 13 Real functions (26-XX) 13 Global analysis, analysis on manifolds (58-XX) 11 Partial differential equations (35-XX) 6 Measure and integration (28-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 5 General and overarching topics; collections (00-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 Harmonic analysis on Euclidean spaces (42-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 118 Publications have been cited 885 times in 339 Documents Cited by ▼ Year ▼ Geometry of Carnot-Carathéodory spaces and differentiability of mappings. Zbl 1146.53023Vodopyanov, S. K. 56 2007 Geometry of Carnot-Carathéodory spaces differentiability, coarea and area formulas. Zbl 1297.53029Karmanova, Maria; Vodop’yanov, Sergey 53 2009 Set functions and their applications in the theory of Lebesgue and Sobolev spaces. I. Zbl 1089.47027Vodop’yanov, S. K.; Ukhlov, A. D. 30 2004 Regularity of mappings inverse to Sobolev mappings. Zbl 1266.26019Vodop’yanov, S. K. 27 2012 Superposition operators in Sobolev spaces. Zbl 1033.47020Vodop’yanov, S. K.; Ukhlov, A. D. 27 2002 Approximate differentiability of mappings of Carnot-Carathéodory spaces. Zbl 1293.53041Basalaev, S. G.; Vodopyanov, S. K. 25 2013 Sobolev spaces and \((P,Q)\)-quasiconformal mappings of Carnot groups. Zbl 0917.46023Vodop’yanov, S. K.; Ukhlov, A. D. 24 1998 \(\mathcal P\)-differentiability on Carnot groups in different topologies and related topics. Zbl 0992.58005Vodop’yanov, Serguei K. 24 2000 Monotone functions and quasiconformal mappings on Carnot groups. Zbl 0876.30020Vodop’yanov, S. K. 22 1996 Quasiconformal mappings and spaces of functions with generalized first derivatives. Zbl 0353.30019Vodop’yanov, S. K.; Gol’dshtejn, V. M. 20 1977 Mappings with bounded \((P,Q)\)-distortion on Carnot groups. Zbl 1213.30049Ukhlov, A.; Vodop’yanov, S. K. 18 2010 Mappings associated with weighted Sobolev spaces. Zbl 1166.30012Ukhlov, A.; Vodopyanov, S. K. 18 2008 On geometric properties of functions with generalized first derivatives. Zbl 0429.30017Vodop’yanov, S. K.; Gol’dshteĭn, V. M.; Reshetnyak, Yu. G. 18 1979 Lattice isomorphisms of the spaces \(W^1_n\) and quasiconformal mappings. Zbl 0324.46040Vodop’yanov, S. K.; Gol’dshtejn, V. M. 17 1975 A coarea formula for smooth contact mappings of Carnot-Carathéodory spaces. Zbl 1304.53024Karmanova, M.; Vodopyanov, S. 16 2013 A classification of sub-Riemannian manifolds. Zbl 0937.31013Vodop’yanov, S. K.; Markina, I. G. 16 1998 Superposition operators in the Lebesgue spaces and differentiability of quasiadditive set functions. Zbl 1050.47031Vodopyanov, S. K.; Ukhlov, A. D. 14 2002 Mappings of homogeneous groups and imbeddings of functional spaces. Zbl 0731.46019Vodop’yanov, S. K. 13 1989 Liouville type theorems for mappings with bounded (co)-distortion. Zbl 1019.30022Troyanov, Marc; Vodop’yanov, Sergei 13 2002 Approximately differentiable transformations and change of variables on nilpotent groups. Zbl 0870.43005Vodop’yanov, S. K.; Ukhlov, A. D. 12 1996 Isomorphisms of Sobolev spaces on Carnot groups and quasi-isometric mappings. Zbl 1322.46025Vodop’yanov, S. K.; Evseev, N. A. 12 2014 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. 11 1995 Sobolev spaces and hypoelliptic equations. Zbl 0925.46011Vodop’yanov, S. K.; Chernikov, V. M. 11 1995 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 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. 11 1979 Coercive estimates and integral representation formulas on Carnot groups. Zbl 1219.43007Isangulova, D. V.; Vodopyanov, S. K. 10 2010 Prolongement de fonctions différentiables hors de domaines plans. Zbl 0482.46019Gol’dstein, Vladimir; Vodop’janov, Serge 10 1981 On local approximation theorem on equiregular Carnot-Carathéodory spaces. Zbl 1294.53032Karmanova, Maria; Vodopyanov, Sergey 9 2014 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. 9 1977 Set functions and their applications in the theory of Lebesgue and Sobolev spaces. I. Zbl 1050.47030Vodopyanov, S. K.; Ukhlov, A. D. 9 2003 Injectivity almost everywhere and mappings with finite distortion in nonlinear elasticity. Zbl 1430.30011Molchanova, Anastasia; Vodopyanov, Sergey 9 2020 Sub-Riemannian geometry for vector fields of minimal smoothness. Zbl 1184.53035Vodop’yanov, S. K.; Karmanova, M. B. 8 2008 Spaces of differential forms and maps with controlled distortion. Zbl 1203.46025Vodop’yanov, S. K. 8 2010 Composition operators on Sobolev spaces. Zbl 1098.46027Vodopyanov, S. K. 8 2005 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. 8 2000 On the regularity of the Poletskii function under weak analytic assumptions on the given mapping. Zbl 1305.26031Vodop’yanov, S. K. 8 2014 An area formula for \(C^{1}\)-smooth contact mappings of Carnot manifolds. Zbl 1180.53035Vodop’yanov, S. K.; Karmanova, M. B. 7 2008 On the differentiability of mappings of Carnot-Carathéodory spaces. Zbl 1246.30043Vodop’yanov, S. K.; Greshnov, A. V. 7 2003 On regularity of mappings inverse to Sobolev mappings. Zbl 1234.30023Vodop’yanov, S. K. 7 2008 Superposition operators in Sobolev spaces. Zbl 1246.30044Vodop’yanov, S. K.; Ukhlov, A. D. 7 2002 Sharp geometric rigidity of isometries on Heisenberg groups. Zbl 1279.53030Isangulova, D. V.; Vodopyanov, S. K. 7 2013 Basics of the quasiconformal analysis of a two-index scale of spatial mappings. Zbl 1415.30022Vodopyanov, S. K. 7 2018 Differentiability of mappings of the Sobolev space \(W_{n-1}^1\) with conditions on the distortion function. Zbl 1412.30094Vodopyanov, S. K. 7 2018 Differentiability of curves in the category of Carnot manifolds. Zbl 1134.53017Vodop’yanov, S. K. 6 2006 Taylor’s formula and function spaces. Textbook. (Формула Тейлора и функционалъные пространства. Учебное пособие.) Zbl 0709.46009Vodop’yanov, S. K. 6 1988 An area formula for contact \(C^{1}\)-mappings of Carnot manifolds. Zbl 1193.51015Karmanova, Maria; Vodopyanov, Sergey 6 2010 Foundations of the theory of mappings with bounded distortion on Carnot groups. Zbl 1146.53045Vodopyanov, S. K. 6 2007 Mappings with bounded distortion and with finite distortion on Carnot groups. Zbl 0973.30021Vodop’yanov, S. K. 6 1998 Potential theory on homogeneous groups. Zbl 0673.31005Vodop’yanov, S. K. 6 1989 A coarea formula for smooth contact mappings of Carnot manifolds. Zbl 1153.53056Vodop’yanov, S. K.; Karmanova, M. B. 6 2007 Functional characteristics of quasiisometric mappings. Zbl 0389.30014Vodop’yanov, S. K.; Gol’dshtejn, V. M. 6 1977 Weighted Sobolev spaces and boundary behavior of solutions to degenerate hypoelliptic equations. Zbl 0878.46024Vodop’yanov, S. K. 5 1995 Closure of classes of mappings with bounded distortion on Carnot groups. Zbl 1076.30025Vodop’yanov, S. K. 5 2004 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 quasiconformal mappings. Zbl 1348.46045Vodop’yanov, S. K.; Evseev, N. A. 5 2015 On grand Sobolev spaces and pointwise description of Banach function spaces. Zbl 1464.46031Jain, Pankaj; Molchanova, Anastasia; Singh, Monika; Vodopyanov, Sergey 5 2021 Weighted \(L_ p\)-potential theory on homogeneous groups. Zbl 0787.31012Vodop’yanov, S. K. 4 1992 Whitney-type theorems on extension of functions on Carnot groups. Zbl 1155.30346Vodopyanov, S. K.; Pupyshev, I. M. 4 2006 On admissible changes of variables for Sobolev functions on (sub)Riemannian manifolds. Zbl 1365.46030Vodopyanov, S. K. 4 2016 Isomorphisms of Sobolev spaces on Carnot groups and metric properties of mappings. Zbl 1348.46044Vodop’yanov, S. K.; Evseev, N. A. 4 2015 Variational problems of nonlinear elasticity in certain classes of mappings with finite distortion. Zbl 1336.49017Vodop’yanov, S. K.; Molchanova, A. O. 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 Set functions and their applications in the theory of Lebesgue and Sobolev spaces. II. Zbl 1091.47027Vodop’yanov, S. K.; Ukhlov, A. D. 4 2005 Admissible changes of variables for Sobolev functions on (sub-)Riemannian manifolds. Zbl 1422.58002Vodopyanov, S. K. 4 2019 Functional characteristics of quasi-isometric mappings. Zbl 0364.30030Vodop’yanov, S. K.; Gol’dshtejn, V. M. 3 1976 Potential theory on homogeneous groups. Zbl 0695.31009Vodop’yanov, S. K. 3 1990 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 Differentiability of mappings in the geometry of Carnot manifolds. Zbl 1164.53345Vodop’yanov, S. K. 3 2007 Kriterium der Fortsetzung von Funktionen der Klasse \(L^1_2\) aus unbeschränkten ebenen Gebieten. Zbl 0416.30014Vodop’yanov, S. K.; Gol’dshtejn, V. M.; Latfullin, T. G. 3 1979 Foundations of quasiconformal analysis of a two-index scale of spatial mappings. Zbl 1418.30015Vodopyanov, S. K. 3 2019 Lower semicontinuity of mappings with bounded \((\theta, 1)\)-weighted \((p,q)\)-distortion. Zbl 1359.30040Vodop’yanov, S. K.; Molchanova, A. O. 3 2016 Isomorphisms of Sobolev spaces on Riemannian manifolds and quasiconformal mappings. Zbl 1444.46029Vodopyanov, S. K. 3 2019 Sobolev \(W^1_p\)-spaces on \(d\)-thick closed subsets of \({\mathbb{R}}^n \). Zbl 1462.46044Vodopyanov, S. K.; Tyulenev, A. I. 3 2020 The regularity of inverses to Sobolev mappings and the theory of \(\mathcal{Q}_{q,p} \)-homeomorphisms. Zbl 1456.30046Vodopyanov, S. K. 3 2020 Composition operators on weighted Sobolev spaces and the theory of \(\mathcal{Q}_p\)-homeomorphisms. Zbl 1477.30053Vodopyanov, S. K. 3 2020 Verbandsisomorphismen der \(W^1_n\)-Räume und quasikonforme Abbildungen. Zbl 0309.46029Vodop’yanov, S. K.; Gol’dshtejn, V. M. 2 1975 Quasikonforme Abbildungen und Räume von Funktionen mit rechtsseitigen verallgemeinerten Ableitungen. Zbl 0339.30018Vodop’yanov, S. K.; Gol’dshtejn, V. M. 2 1976 Weighted Sobolev spaces and quasiconformal mappings. Zbl 1127.46023Vodop’yanov, S. K.; Ukhlov, A. D. 2 2005 Differentiability of mappings of Carnot manifolds and isomorphism of tangent cones. Zbl 1206.53037Vodop’yanov, S. K. 2 2006 Normal families of mappings on Carnot groups. Zbl 0876.30021Vodop’yanov, S. K.; Kudryavtseva, N. A. 2 1996 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 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 On closedness of classes of mappings with bounded distortion on Carnot groups. Zbl 1015.30008Vodop’yanov, S. K. 2 2002 Prolongement des fonctions de classe \(R^ n\) et applications quasi conformes. Zbl 0451.30014Gol’dstein, Vladimir Mikailovitch; Vodop’janov, Sergei Konstantinovitch 2 1980 Functional and analytic properties of a class of mappings in quasi-conformal analysis. Zbl 1486.30074Vodopyanov, S. K.; Tomilov, A. O. 2 2021 On the Whitney problem for weighted Sobolev spaces. Zbl 06731613Tyulenev, A. I.; Vodop’yanov, S. K. 2 2017 On the analytic and geometric properties of mappings in the theory of \(\mathscr{Q}_{q,p}\)-homeomorphisms. Zbl 1457.30007Vodop’yanov, S. K. 2 2020 On the convergence of mappings with \(k\)-finite distortion. Zbl 1393.30020Vodop’yanov, S. K.; Kudryavtseva, N. A. 2 2017 Algebraic properties of the tangent cone to a quasimetric space with dilations. Zbl 1198.53033Vodop’yanov, S. K.; Selivanova, S. V. 1 2009 Sharp bounds for geometric rigidity of isometries on Heisenberg groups. Zbl 1160.43005Vodop’yanov, S. K.; Isangulova, D. V. 1 2008 L\({}_ p\)-potential theory for generalized kernels. Zbl 0716.31003Vodop’yanov, S. K. 1 1990 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 Whitney-type theorems on extension of functions on Carnot groups. Zbl 1150.30334Vodop’yanov, S. K.; Pupyshev, I. M. 1 2006 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 Exceptional sets for solutions to subelliptic equations. Zbl 0858.35026Vodop’yanov, S. K.; Markina, I. G. 1 1995 On grand Sobolev spaces and pointwise description of Banach function spaces. Zbl 1464.46031Jain, Pankaj; Molchanova, Anastasia; Singh, Monika; Vodopyanov, Sergey 5 2021 Functional and analytic properties of a class of mappings in quasi-conformal analysis. Zbl 1486.30074Vodopyanov, S. K.; Tomilov, A. O. 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 Injectivity almost everywhere and mappings with finite distortion in nonlinear elasticity. Zbl 1430.30011Molchanova, Anastasia; Vodopyanov, Sergey 9 2020 Sobolev \(W^1_p\)-spaces on \(d\)-thick closed subsets of \({\mathbb{R}}^n \). Zbl 1462.46044Vodopyanov, S. K.; Tyulenev, A. I. 3 2020 The regularity of inverses to Sobolev mappings and the theory of \(\mathcal{Q}_{q,p} \)-homeomorphisms. Zbl 1456.30046Vodopyanov, S. K. 3 2020 Composition operators on weighted Sobolev spaces and the theory of \(\mathcal{Q}_p\)-homeomorphisms. Zbl 1477.30053Vodopyanov, S. K. 3 2020 On the analytic and geometric properties of mappings in the theory of \(\mathscr{Q}_{q,p}\)-homeomorphisms. Zbl 1457.30007Vodop’yanov, S. K. 2 2020 Admissible changes of variables for Sobolev functions on (sub-)Riemannian manifolds. Zbl 1422.58002Vodopyanov, S. K. 4 2019 Foundations of quasiconformal analysis of a two-index scale of spatial mappings. Zbl 1418.30015Vodopyanov, S. K. 3 2019 Isomorphisms of Sobolev spaces on Riemannian manifolds and quasiconformal mappings. Zbl 1444.46029Vodopyanov, S. K. 3 2019 Basics of the quasiconformal analysis of a two-index scale of spatial mappings. Zbl 1415.30022Vodopyanov, S. K. 7 2018 Differentiability of mappings of the Sobolev space \(W_{n-1}^1\) with conditions on the distortion function. Zbl 1412.30094Vodopyanov, S. K. 7 2018 On the Whitney problem for weighted Sobolev spaces. Zbl 06731613Tyulenev, A. I.; Vodop’yanov, S. K. 2 2017 On the convergence of mappings with \(k\)-finite distortion. Zbl 1393.30020Vodop’yanov, S. K.; Kudryavtseva, N. A. 2 2017 On admissible changes of variables for Sobolev functions on (sub)Riemannian manifolds. Zbl 1365.46030Vodopyanov, S. K. 4 2016 Lower semicontinuity of mappings with bounded \((\theta, 1)\)-weighted \((p,q)\)-distortion. Zbl 1359.30040Vodop’yanov, S. K.; Molchanova, A. O. 3 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 quasiconformal mappings. Zbl 1348.46045Vodop’yanov, S. K.; Evseev, N. A. 5 2015 Isomorphisms of Sobolev spaces on Carnot groups and metric properties of mappings. Zbl 1348.46044Vodop’yanov, S. K.; Evseev, N. A. 4 2015 Variational problems of nonlinear elasticity in certain classes of mappings with finite distortion. Zbl 1336.49017Vodop’yanov, S. K.; Molchanova, A. O. 4 2015 Isomorphisms of Sobolev spaces on Carnot groups and quasi-isometric mappings. Zbl 1322.46025Vodop’yanov, S. K.; Evseev, N. A. 12 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. 25 2013 A coarea formula for smooth contact mappings of Carnot-Carathéodory spaces. Zbl 1304.53024Karmanova, M.; Vodopyanov, S. 16 2013 Sharp geometric rigidity of isometries on Heisenberg groups. Zbl 1279.53030Isangulova, D. V.; Vodopyanov, S. K. 7 2013 Regularity of mappings inverse to Sobolev mappings. Zbl 1266.26019Vodop’yanov, S. K. 27 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. 18 2010 Coercive estimates and integral representation formulas on Carnot groups. Zbl 1219.43007Isangulova, D. V.; Vodopyanov, S. K. 10 2010 Spaces of differential forms and maps with controlled distortion. Zbl 1203.46025Vodop’yanov, S. K. 8 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 53 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 Sub-Riemannian geometry for vector fields of minimal smoothness. Zbl 1184.53035Vodop’yanov, S. K.; Karmanova, M. B. 8 2008 An area formula for \(C^{1}\)-smooth contact mappings of Carnot manifolds. Zbl 1180.53035Vodop’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 Sobolev classes of mappings on a Carnot-Carathéodory space: various norms and variational problems. Zbl 1224.46071Vodop’yanov, S. K.; Romanovskij, N. N. 1 2008 Geometry of Carnot-Carathéodory spaces and differentiability of mappings. Zbl 1146.53023Vodopyanov, S. K. 56 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 mappings in the geometry of Carnot manifolds. Zbl 1164.53345Vodop’yanov, S. K. 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 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 Whitney-type theorems on extension of functions on Carnot groups. Zbl 1150.30334Vodop’yanov, S. K.; Pupyshev, I. M. 1 2006 Composition operators on Sobolev spaces. Zbl 1098.46027Vodopyanov, S. K. 8 2005 Set functions and their applications in the theory of Lebesgue and Sobolev spaces. II. Zbl 1091.47027Vodop’yanov, S. K.; Ukhlov, A. D. 4 2005 Weighted Sobolev spaces and quasiconformal mappings. Zbl 1127.46023Vodop’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. 30 2004 Closure of classes of mappings with bounded distortion on Carnot groups. Zbl 1076.30025Vodop’yanov, S. K. 5 2004 Set functions and their applications in the theory of Lebesgue and Sobolev spaces. I. Zbl 1050.47030Vodopyanov, S. K.; Ukhlov, A. D. 9 2003 On the differentiability of mappings of Carnot-Carathéodory spaces. Zbl 1246.30043Vodop’yanov, S. K.; Greshnov, A. V. 7 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. 27 2002 Superposition operators in the Lebesgue spaces and differentiability of quasiadditive set functions. Zbl 1050.47031Vodopyanov, S. K.; Ukhlov, A. D. 14 2002 Liouville type theorems for mappings with bounded (co)-distortion. Zbl 1019.30022Troyanov, Marc; Vodop’yanov, Sergei 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. 24 2000 Topological and geometrical properties of mappings with summable Jacobian in Sobolev classes. I. Zbl 0983.30009Vodop’yanov, S. K. 8 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. 24 1998 A classification of sub-Riemannian manifolds. Zbl 0937.31013Vodop’yanov, S. K.; Markina, I. G. 16 1998 Mappings with bounded distortion and with finite distortion on Carnot groups. Zbl 0973.30021Vodop’yanov, S. K. 6 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. 22 1996 Approximately differentiable transformations and change of variables on nilpotent groups. Zbl 0870.43005Vodop’yanov, S. K.; Ukhlov, A. D. 12 1996 Normal families of mappings on Carnot groups. Zbl 0876.30021Vodop’yanov, S. K.; Kudryavtseva, N. A. 2 1996 Quasiconformal mappings on Carnot groups and their applications. Zbl 0896.30016Vodop’yanov, S. K. 1 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. 11 1995 Sobolev spaces and hypoelliptic equations. Zbl 0925.46011Vodop’yanov, S. K.; Chernikov, V. M. 11 1995 Weighted Sobolev spaces and boundary behavior of solutions to degenerate hypoelliptic equations. Zbl 0878.46024Vodop’yanov, S. K. 5 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. 3 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. 13 1989 Potential theory on homogeneous groups. Zbl 0673.31005Vodop’yanov, S. K. 6 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 Maximum principle in potential theory and imbedding theorems for anisotropic spaces of differentiable functions. Zbl 0699.31019Vodop’yanov, S. K. 1 1988 Quasielliptic \(L_ p\)-potential theory and its applications. Zbl 0706.31006Vodop’yanov, S. K. 1 1988 The maximum principle in potential theory and imbedding theorems for anisotropic spaces of differentiable functions. Zbl 0646.31010Vodop’yanov, S. K. 1 1988 Equivalent normalizations of Sobolev and Nikol’skiĭ spaces in domains. Boundary values and extension. Zbl 0646.46028Vodop’yanov, S. K. 1 1988 ...and 18 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 231 Authors 56 Karmanova, Maria B. 49 Vodop’yanov, Sergeĭ Konstantinovich 31 Ukhlov, Alexander Dadar-Oolovich 23 Gol’dshtein, Vladimir Mikhailovich 11 Evseev, Nikita Aleksandrovich 11 Sevost’yanov, Yevgen Oleksandrovych 9 Ryazanov, Vladimir Il’ich 8 Isangulova, D. V. 7 Basalaev, Sergey G. 7 Greshnov, Aleksandr Valer’evich 7 Koskela, Pekka 7 Pchelintsev, Valery Anatol’evich 7 Salimov, Ruslan Radikovich 6 Markina, Irina 6 Molchanova, Anastasia Olegovna 6 Selivanova, Svetlana V. 6 Tryamkin, Maksim Vladimirovich 5 Morbidelli, Daniele 5 Tyulenev, Alexander I. 4 Gutlyanskiĭ, Vladimir Ya. 4 Menovshchikov, A. V. 4 Zhou, Yuan 3 Björn, Anders 3 Dymchenko, Yuriĭ Viktorovich 3 Garofalo, Nicola 3 Heinonen, Juha 3 Menovschikov, Alexander 3 Monti, Roberto 3 Müller, Stefan 3 Shanmugalingam, Nageswari 3 Troyanov, Marc 3 Zobin, Nahum 2 Battaglia, Erika 2 Bilalov, Bilal T. 2 Bramanti, Marco 2 Buckley, Stephen M. 2 Capogna, Luca 2 Cetin, Seyma 2 Fässler, Katrin S. 2 Franchi, Bruno 2 Garain, Prashanta 2 Henao, Duvan A. 2 Hurri-Syrjānen, Ritva 2 Kleprlík, Luděk 2 Kovtonyuk, D. A. 2 Kovtonyuk, Denis 2 Kudryavtseva, N. A. 2 Lomako, Tetiana 2 Martin, Gaven J. 2 Martio, Olli 2 Montanari, Annamaria 2 Montefalcone, Francescopaolo 2 Nhieu, Duy-Minh 2 Onninen, Jani 2 Peltonen, Kirsi 2 Romanovskii, N. N. 2 Sadigova, Sabina Rahib 2 Serra Cassano, Francesco 2 Shvartsman, Pavel 2 Sivaloganathan, Jeyabal 2 Spector, Scott J. 2 Stroffolini, Bianca 2 Vittone, Davide 2 Xiao, Jie 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, Jana 1 Bogachev, Vladimir Igorevich 1 Bojarski, Bogdan 1 Bonfiglioli, Andrea 1 Bouali, Bouchta 1 Brakalova, Melkana Aleksandrova 1 Brandolini, Luca 1 Brewster, Kevin 1 Bukhvalov, Alexander V. 1 Buliga, Marius G. 1 Charifi, Ahmed 1 Chebanenko, Nikita Alekseevich 1 Choudhuri, Debajyoti 1 Christ, Michael 1 Ciarlet, Philippe Gaston 1 Cinti, Eleonora 1 Citti, Giovanna 1 Corni, Francesca 1 Cowling, Michael G. 1 Danielli, Donatella 1 Davoli, Elisa 1 De Cicco, Virginia 1 Du, Hengrong 1 Egorov, Aleksandr Anatol’evich ...and 131 more Authors all top 5 Cited in 88 Serials 65 Siberian Mathematical Journal 48 Doklady Mathematics 18 Journal of Mathematical Sciences (New York) 11 Journal of Mathematical Analysis and Applications 9 Journal d’Analyse Mathématique 9 Mathematical Notes 9 Journal of Functional Analysis 8 Archive for Rational Mechanics and Analysis 8 The Journal of Geometric Analysis 7 Calculus of Variations and Partial Differential Equations 6 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 6 Russian Mathematics 6 Complex Variables and Elliptic Equations 5 St. Petersburg Mathematical Journal 4 Mathematische Zeitschrift 4 Vladikavkazskiĭ Matematicheskiĭ Zhurnal 3 Advances in Mathematics 3 Mathematische Annalen 3 Proceedings of the American Mathematical Society 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 Sibirskie Èlektronnye Matematicheskie Izvestiya 3 Complex Analysis and Operator Theory 3 Analysis and Mathematical Physics 3 Transactions of A. Razmadze Mathematical Institute 2 Arkiv för Matematik 2 Acta Mathematica 2 Annales de l’Institut Fourier 2 Journal of Soviet Mathematics 2 Mathematische Nachrichten 2 Geometric and Functional Analysis. GAFA 2 Georgian Mathematical Journal 2 Sbornik: Mathematics 2 Izvestiya: Mathematics 2 Matematicheskie Trudy 2 Lobachevskii Journal of Mathematics 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 2 Proceedings of the Steklov Institute of Mathematics 2 Forum of Mathematics, Sigma 2 Analysis and Geometry in Metric Spaces 2 Annales Fennici Mathematici 1 Israel Journal of Mathematics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Moscow University Mathematics Bulletin 1 Ukrainian Mathematical Journal 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. 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Mathematica 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 Advances in Calculus of Variations 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 Nonlinear Analysis. Theory, Methods & Applications 1 Bollettino dell’Unione Matematica Italiana 1 Constructive Mathematical Analysis all top 5 Cited in 35 Fields 124 Functions of a complex variable (30-XX) 108 Functional analysis (46-XX) 96 Differential geometry (53-XX) 67 Partial differential equations (35-XX) 36 Calculus of variations and optimal control; optimization (49-XX) 26 Global analysis, analysis on manifolds (58-XX) 23 Real functions (26-XX) 23 Operator theory (47-XX) 22 Topological groups, Lie groups (22-XX) 18 Potential theory (31-XX) 17 Abstract harmonic analysis (43-XX) 15 Mechanics of deformable solids (74-XX) 14 Measure and integration (28-XX) 11 Harmonic analysis on Euclidean spaces (42-XX) 7 General topology (54-XX) 6 Geometry (51-XX) 5 Several complex variables and analytic spaces (32-XX) 3 Convex and discrete geometry (52-XX) 3 Manifolds and cell complexes (57-XX) 2 Combinatorics (05-XX) 2 Nonassociative rings and algebras (17-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Numerical analysis (65-XX) 2 Computer science (68-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Difference and functional equations (39-XX) 1 Algebraic topology (55-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Operations research, mathematical programming (90-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