Edit Profile Vodop’yanov, Sergeĭ Konstantinovich Compute Distance To: Compute Author ID: vodopyanov.serguei-k Published as: Vodop’janov, S. K.; Vodop’janov, Serge; Vodop’janov, Sergei Konstantinovitch; Vodop’yanov, S. K.; Vodop’yanov, Sergei; Vodop’yanov, Sergej K.; Vodop’yanov, Sergey; Vodop’yanov, Serguei; Vodop’yanov, Serguei K.; Vodopjanov, S. K.; Vodopyanov, S.; Vodopyanov, S. K.; Vodopyanov, Sergey External Links: MGP · Math-Net.Ru Documents Indexed: 168 Publications since 1970, including 6 Books all top 5 Co-Authors 64 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 Gordon, Evgeniĭ Izrail’evich 4 Kudryavtseva, N. A. 4 Latfullin, T. G. 4 Molchanova, Anastasia Olegovna 3 Evseev, Nikita Aleksandrovich 3 Gol’dstein, Vladimir Mikailovitch 3 Kusraev, Anatoly Georgievich 3 Vesnin, Andrei Yu. 2 Bokut, Leonid A. 2 Gol’dshtein, Vladimir Mikhailovich 2 Gutman, A. E. 2 Karmanova, M. V. 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, A. I. 2 Valiev, Mars K. 1 Abanin, Aleksandr Vasil’evich 1 Alborova, M. S. 1 Alexandrov, Victor A. 1 Archangelsky, Dmitry 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 Belonogov, Vyacheslav Aleksandrovich 1 Belyaev, V. Ya. 1 Beresmovskiĭ, V. N. 1 Borisenko, A. A. jun. 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 Dekhtyar, Mikhail I. 1 Dikovsky, Alexander Yakovlevich 1 Dubinin, Vladimir N. 1 Dudakov, Sergey M. 1 Gitik, Moti 1 Gol’dshteyn, V. M. 1 Goryainov, Viktor V. 1 Grigor’yan, Alexander Asaturovich 1 Gurevich, Yuri 1 Gutman, Aleksandr Efimovich 1 Iwaniec, Tadeusz 1 Jain, Pankaj 1 Kesel’man, V. M. 1 Khudalov, Marat Zakharovich 1 Klimentov, S. B. 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 Fedorovich 1 Krushkal, Samuel L. 1 Kutatetadse, S. S. 1 Kuz’minov, Vladimir I. 1 Kysmunych, A. V. 1 Loboda, Alexander Vasil’evich 1 Losev, Alexander G. 1 Ludnik, V. G. 1 Makhnev, Aleksandr Aleksandrovich jun. 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 Semenov, Alexei Lvovich 1 Sergeev, Armen Glebovich 1 Singh, Monika 1 Slavskiĭ, Viktor Vladimirovich 1 Stolboushkin, Alexei P. ...and 15 more Co-Authors all top 5 Serials 37 Doklady Mathematics 32 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 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 Izvestiya: Mathematics 1 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 1 Complex Variables and Elliptic Equations 1 Contemporary Mathematics 1 Problemy Analiza. Issues of Analysis all top 5 Fields 84 Functions of a complex variable (30-XX) 78 Functional analysis (46-XX) 32 Potential theory (31-XX) 24 Topological groups, Lie groups (22-XX) 24 Differential geometry (53-XX) 23 Abstract harmonic analysis (43-XX) 13 Global analysis, analysis on manifolds (58-XX) 12 Operator theory (47-XX) 11 History and biography (01-XX) 10 Real functions (26-XX) 10 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 98 Publications have been cited 695 times in 273 Documents Cited by ▼ Year ▼ Geometry of Carnot-Carathéodory spaces differentiability, coarea and area formulas. Zbl 1297.53029Karmanova, Maria; Vodop’yanov, Sergey 46 2009 Geometry of Carnot-Carathéodory spaces and differentiability of mappings. Zbl 1146.53023Vodopyanov, S. K. 44 2007 Quasiconformal mappings and spaces of functions with generalized first derivatives. Zbl 0353.30019Vodop’yanov, S. K.; Gol’dshtejn, V. M. 24 1977 Superposition operators in Sobolev spaces. Zbl 1033.47020Vodop’yanov, S. K.; Ukhlov, A. D. 23 2002 Approximate differentiability of mappings of Carnot-Carathéodory spaces. Zbl 1293.53041Basalaev, S. G.; Vodopyanov, S. K. 21 2013 Regularity of mappings inverse to Sobolev mappings. Zbl 1266.26019Vodop’yanov, S. K. 21 2012 Set functions and their applications in the theory of Lebesgue and Sobolev spaces. I. Zbl 1089.47027Vodop’yanov, S. K.; Ukhlov, A. D. 20 2004 Sobolev spaces and \((P,Q)\)-quasiconformal mappings of Carnot groups. Zbl 0917.46023Vodop’yanov, S. K.; Ukhlov, A. D. 20 1998 \(\mathcal P\)-differentiability on Carnot groups in different topologies and related topics. Zbl 0992.58005Vodop’yanov, Serguei K. 19 2000 Monotone functions and quasiconformal mappings on Carnot groups. Zbl 0876.30020Vodop’yanov, S. K. 17 1996 Mappings associated with weighted Sobolev spaces. Zbl 1166.30012Ukhlov, A.; Vodopyanov, S. K. 16 2008 Mappings with bounded \((P,Q)\)-distortion on Carnot groups. Zbl 1213.30049Ukhlov, A.; Vodop’yanov, S. K. 15 2010 A classification of sub-Riemannian manifolds. Zbl 0937.31013Vodop’yanov, S. K.; Markina, I. G. 14 1998 Lattice isomorphisms of the spaces \(W^1_n\) and quasiconformal mappings. Zbl 0324.46040Vodop’yanov, S. K.; Gol’dshtejn, V. M. 13 1975 Liouville type theorems for mappings with bounded (co)-distortion. Zbl 1019.30022Troyanov, Marc; Vodop’yanov, Sergei 12 2002 On geometric properties of functions with generalized first derivatives. Zbl 0429.30017Vodop’yanov, S. K.; Gol’dshteĭn, V. M.; Reshetnyak, Yu. G. 12 1979 Local geometry of Carnot manifolds under minimal smoothness. Zbl 1175.53046Vodop’yanov, S. K.; Karmanova, M. B. 11 2007 Superposition operators in the Lebesgue spaces and differentiability of quasiadditive set functions. Zbl 1050.47031Vodopyanov, S. K.; Ukhlov, A. D. 11 2002 Analytic properties of quasiconformal mappings on Carnot groups. Zbl 0891.30013Vodop’yanov, S. K.; Greshnov, A. V. 11 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. 11 1979 A coarea formula for smooth contact mappings of Carnot-Carathéodory spaces. Zbl 1304.53024Karmanova, M.; Vodopyanov, S. 10 2013 Capacity estimates, Liouville’s theorem, and singularity removal for mappings with bounded \((p,q)\)-distortion. Zbl 1341.30016Baykin, A. N.; Vodop’yanov, S. K. 9 2015 Isomorphisms of Sobolev spaces on Carnot groups and quasi-isometric mappings. Zbl 1322.46025Vodop’yanov, S. K.; Evseev, N. A. 9 2014 On local approximation theorem on equiregular Carnot-Carathéodory spaces. Zbl 1294.53032Karmanova, Maria; Vodopyanov, Sergey 9 2014 Approximately differentiable transformations and change of variables on nilpotent groups. Zbl 0870.43005Vodop’yanov, S. K.; Ukhlov, A. D. 9 1996 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 Coercive estimates and integral representation formulas on Carnot groups. Zbl 1219.43007Isangulova, D. V.; Vodopyanov, S. K. 8 2010 A local approximation theorem on Carnot manifolds under minimal smoothness conditions. Zbl 1188.53029Vodop’yanov, S. K.; Karmanova, M. V. 8 2009 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 with bounded distortion and with finite distortion on Carnot groups. Zbl 0973.30021Vodop’yanov, S. K. 8 1998 Mappings of homogeneous groups and imbeddings of functional spaces. Zbl 0731.46019Vodop’yanov, S. K. 8 1989 Prolongement de fonctions différentiables hors de domaines plans. Zbl 0482.46019Gol’dstein, Vladimir; Vodop’janov, Serge 8 1981 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 On the regularity of the Poletskii function under weak analytic assumptions on the given mapping. Zbl 1305.26031Vodop’yanov, S. K. 7 2014 On regularity of mappings inverse to Sobolev mappings. Zbl 1234.30023Vodop’yanov, S. K. 7 2008 Sub-Riemannian geometry for vector fields of minimal smoothness. Zbl 1184.53035Vodop’yanov, S. K.; Karmanova, M. B. 7 2008 An area formula for \(C^{1}\)-smooth contact mappings of Carnot manifolds. Zbl 1180.53035Vodop’yanov, S. K.; Karmanova, M. B. 7 2008 Topological and geometrical properties of mappings with summable Jacobian in Sobolev classes. I. Zbl 0983.30009Vodop’yanov, S. K. 7 2000 Sharp geometric rigidity of isometries on Heisenberg groups. Zbl 1279.53030Isangulova, D. V.; Vodopyanov, S. K. 6 2013 Spaces of differential forms and maps with controlled distortion. Zbl 1203.46025Vodop’yanov, S. K. 6 2010 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 Foundations of the theory of mappings with bounded distortion on Carnot groups. Zbl 1146.53045Vodopyanov, S. K. 6 2007 Differentiability of curves in the category of Carnot manifolds. Zbl 1134.53017Vodop’yanov, S. K. 6 2006 Composition operators on Sobolev spaces. Zbl 1098.46027Vodopyanov, S. K. 6 2005 Superposition operators in Sobolev spaces. Zbl 1246.30044Vodop’yanov, S. K.; Ukhlov, A. D. 6 2002 Functional characteristics of quasiisometric mappings. Zbl 0389.30014Vodop’yanov, S. K.; Gol’dshtejn, V. M. 6 1977 On value distributions for quasimeromorphic mappings on \(\mathbb H\)-type Carnot groups. Zbl 1110.32006Markina, Irina; Vodopyanov, Sergey 5 2006 On the differentiability of mappings of Carnot-Carathéodory spaces. Zbl 1246.30043Vodop’yanov, S. K.; Greshnov, A. V. 5 2003 Taylor’s formula and function spaces. Textbook. Zbl 0709.46009Vodop’yanov, S. K. 5 1988 Prolongement des fonctions de classe \(R^ n\) et applications quasi conformes. Zbl 0451.30014Gol’dstein, Vladimir Mikailovitch; Vodop’janov, Sergei Konstantinovitch 5 1980 Isomorphisms of Sobolev spaces on Carnot groups and metric properties of mappings. Zbl 1348.46044Vodop’yanov, S. K.; Evseev, N. A. 4 2015 Whitney-type theorems on extension of functions on Carnot groups. Zbl 1155.30346Vodopyanov, S. K.; Pupyshev, I. M. 4 2006 Closure of classes of mappings with bounded distortion on Carnot groups. Zbl 1076.30025Vodop’yanov, S. K. 4 2004 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 Potential theory on homogeneous groups. Zbl 0673.31005Vodop’yanov, S. K. 4 1989 Basics of the quasiconformal analysis of a two-index scale of spatial mappings. Zbl 1415.30022Vodopyanov, S. K. 3 2018 Differentiability of mappings of the Sobolev space \(W_{n-1}^1\) with conditions on the distortion function. Zbl 1412.30094Vodopyanov, S. K. 3 2018 Variational problems of nonlinear elasticity in certain classes of mappings with finite distortion. Zbl 1336.49017Vodop’yanov, S. K.; Molchanova, A. O. 3 2015 Mappings of finite codistortion and Sobolev classes of functions. Zbl 1242.26012Vodopyanov, S. K. 3 2011 The interaction of analysis and geometry. International school-conference on analysis and geometry, Novosibirsk, Russia, August 23–September 3, 2004. Zbl 1109.00005Burenkov, V. I. (ed.); Iwaniec, T. (ed.); Vodopyanov, S. K. (ed.) 3 2007 On closedness of classes of mappings with bounded distortion on Carnot groups. Zbl 1015.30008Vodop’yanov, S. K. 3 2002 Injectivity almost everywhere and mappings with finite distortion in nonlinear elasticity. Zbl 1430.30011Molchanova, Anastasia; Vodopyanov, Sergey 2 2020 Admissible changes of variables for Sobolev functions on (sub-)Riemannian manifolds. Zbl 1422.58002Vodopyanov, S. K. 2 2019 On the convergence of mappings with \(k\)-finite distortion. Zbl 1393.30020Vodop’yanov, S. K.; Kudryavtseva, N. A. 2 2017 Lower semicontinuity of mappings with bounded \((\theta, 1)\)-weighted \((p,q)\)-distortion. Zbl 1359.30040Vodop’yanov, S. K.; Molchanova, A. O. 2 2016 On admissible changes of variables for Sobolev functions on (sub)Riemannian manifolds. Zbl 1365.46030Vodopyanov, S. K. 2 2016 Isomorphisms of Sobolev spaces on Carnot groups and quasiconformal mappings. Zbl 1348.46045Vodop’yanov, S. K.; Evseev, N. A. 2 2015 Differentiability of mappings in the geometry of Carnot manifolds. Zbl 1164.53345Vodop’yanov, S. K. 2 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 of Carnot manifolds and isomorphism of tangent cones. Zbl 1206.53037Vodop’yanov, S. K. 2 2006 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 Normal families of mappings on Carnot groups. Zbl 0876.30021Vodop’yanov, S. K.; Kudryavtseva, N. A. 2 1996 Sobolev spaces and hypoelliptic equations. Zbl 0925.46011Vodop’yanov, S. K.; Chernikov, V. M. 2 1995 Weighted Sobolev spaces and boundary behavior of solutions to degenerate hypoelliptic equations. Zbl 0878.46024Vodop’yanov, S. K. 2 1995 Potential theory on homogeneous groups. Zbl 0695.31009Vodop’yanov, S. K. 2 1990 Intrinsic geometries and boundary values of differentiable functions. I. Zbl 0692.46025Vodop’yanov, S. K. 2 1989 Maximum principle in potential theory and imbedding theorems for anisotropic spaces of differentiable functions. Zbl 0699.31019Vodop’yanov, S. K. 2 1988 Isomorphisms of Sobolev spaces on Riemannian manifolds and quasiconformal mappings. Zbl 1444.46029Vodopyanov, S. K. 1 2019 On the Whitney problem for weighted Sobolev spaces. Zbl 06731613Tyulenev, A. I.; Vodop’yanov, S. K. 1 2017 Nonlinear potential theory for Sobolev spaces on Carnot groups. Zbl 1224.46070Vodop’yanov, S. K.; Kudryavtseva, N. A. 1 2009 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 Foundations of the theory of mappings with bounded distortion on Carnot groups. Zbl 1219.30010Vodop’yanov, S. K. 1 2005 Geometry of Carnot-Carathéodory spaces, quasiconformal analysis, and geometric measure theory. Zbl 1048.43011Vodopyanov, S. K. 1 2003 On the closedness of classes of mappings with bounded distortion on Carnot groups. Zbl 1064.30013Vodop’yanov, S. K. 1 2001 Topological properties of mappings from the Sobolev classes with summable Jacobian. Zbl 0961.46019Vodop’yanov, S. K. 1 1998 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 0774.31009Vodop’yanov, S. K. 1 1992 On removable singularities of bounded solutions to quasielliptic equations. Zbl 0791.35023Alborova, M. S.; Vodop’yanov, S. K. 1 1992 L\({}_ p\)-theory of potentials and quasi-conformal mappings on homogeneous groups. Zbl 0714.31005Vodop’yanov, S. K. 1 1989 Equivalent normalizations of Sobolev and Nikol’skiĭ spaces in domains. Boundary values and extension. Zbl 0646.46028Vodop’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 Functional characteristics of quasi-isometric mappings. Zbl 0364.30030Vodop’yanov, S. K.; Gol’dshtejn, V. M. 1 1976 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 Estimates of the deviation from a sphere of quasiumbilical surfaces. Zbl 0214.49205Vodop’yanov, S. K. 1 1971 Injectivity almost everywhere and mappings with finite distortion in nonlinear elasticity. Zbl 1430.30011Molchanova, Anastasia; Vodopyanov, Sergey 2 2020 Admissible changes of variables for Sobolev functions on (sub-)Riemannian manifolds. Zbl 1422.58002Vodopyanov, S. K. 2 2019 Isomorphisms of Sobolev spaces on Riemannian manifolds and quasiconformal mappings. Zbl 1444.46029Vodopyanov, S. K. 1 2019 Basics of the quasiconformal analysis of a two-index scale of spatial mappings. Zbl 1415.30022Vodopyanov, S. K. 3 2018 Differentiability of mappings of the Sobolev space \(W_{n-1}^1\) with conditions on the distortion function. Zbl 1412.30094Vodopyanov, S. K. 3 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. 1 2017 Lower semicontinuity of mappings with bounded \((\theta, 1)\)-weighted \((p,q)\)-distortion. Zbl 1359.30040Vodop’yanov, S. K.; Molchanova, A. O. 2 2016 On admissible changes of variables for Sobolev functions on (sub)Riemannian manifolds. Zbl 1365.46030Vodopyanov, S. K. 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. 9 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. 3 2015 Isomorphisms of Sobolev spaces on Carnot groups and quasiconformal mappings. Zbl 1348.46045Vodop’yanov, S. K.; Evseev, N. A. 2 2015 Isomorphisms of Sobolev spaces on Carnot groups and quasi-isometric mappings. Zbl 1322.46025Vodop’yanov, S. K.; Evseev, N. A. 9 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. 7 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. 10 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. 21 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. 15 2010 Coercive estimates and integral representation formulas on Carnot groups. Zbl 1219.43007Isangulova, D. V.; Vodopyanov, S. K. 8 2010 Spaces of differential forms and maps with controlled distortion. Zbl 1203.46025Vodop’yanov, S. K. 6 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 46 2009 A local approximation theorem on Carnot manifolds under minimal smoothness conditions. Zbl 1188.53029Vodop’yanov, S. K.; Karmanova, M. V. 8 2009 Nonlinear potential theory for Sobolev spaces on Carnot groups. Zbl 1224.46070Vodop’yanov, S. K.; Kudryavtseva, N. A. 1 2009 Algebraic properties of the tangent cone to a quasimetric space with dilations. Zbl 1198.53033Vodop’yanov, S. K.; Selivanova, S. V. 1 2009 Mappings associated with weighted Sobolev spaces. Zbl 1166.30012Ukhlov, A.; Vodopyanov, S. K. 16 2008 On regularity of mappings inverse to Sobolev mappings. Zbl 1234.30023Vodop’yanov, S. K. 7 2008 Sub-Riemannian geometry for vector fields of minimal smoothness. Zbl 1184.53035Vodop’yanov, S. K.; Karmanova, M. B. 7 2008 An area formula for \(C^{1}\)-smooth contact mappings of Carnot manifolds. Zbl 1180.53035Vodop’yanov, S. K.; Karmanova, M. B. 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. 44 2007 Local geometry of Carnot manifolds under minimal smoothness. Zbl 1175.53046Vodop’yanov, S. K.; Karmanova, M. B. 11 2007 A coarea formula for smooth contact mappings of Carnot manifolds. Zbl 1153.53056Vodop’yanov, S. K.; Karmanova, M. B. 6 2007 Foundations of the theory of mappings with bounded distortion on Carnot groups. Zbl 1146.53045Vodopyanov, S. K. 6 2007 The interaction of analysis and geometry. International school-conference on analysis and geometry, Novosibirsk, Russia, August 23–September 3, 2004. Zbl 1109.00005Burenkov, V. I. (ed.); Iwaniec, T. (ed.); Vodopyanov, S. K. (ed.) 3 2007 Differentiability of mappings in the geometry of Carnot manifolds. Zbl 1164.53345Vodop’yanov, S. K. 2 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 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. 20 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. 5 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. 23 2002 Liouville type theorems for mappings with bounded (co)-distortion. Zbl 1019.30022Troyanov, Marc; Vodop’yanov, Sergei 12 2002 Superposition operators in the Lebesgue spaces and differentiability of quasiadditive set functions. Zbl 1050.47031Vodopyanov, S. K.; Ukhlov, A. D. 11 2002 Superposition operators in Sobolev spaces. Zbl 1246.30044Vodop’yanov, S. K.; Ukhlov, A. D. 6 2002 On closedness of classes of mappings with bounded distortion on Carnot groups. Zbl 1015.30008Vodop’yanov, S. K. 3 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. 14 1998 Mappings with bounded distortion and with finite distortion on Carnot groups. Zbl 0973.30021Vodop’yanov, S. K. 8 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. 17 1996 Approximately differentiable transformations and change of variables on nilpotent groups. Zbl 0870.43005Vodop’yanov, S. K.; Ukhlov, A. D. 9 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 Sobolev spaces and hypoelliptic equations. Zbl 0925.46011Vodop’yanov, S. K.; Chernikov, V. M. 2 1995 Weighted Sobolev spaces and boundary behavior of solutions to degenerate hypoelliptic equations. Zbl 0878.46024Vodop’yanov, S. K. 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 Weighted \(L_ p\)-potential theory on homogeneous groups. Zbl 0774.31009Vodop’yanov, S. K. 1 1992 On removable singularities of bounded solutions to quasielliptic equations. Zbl 0791.35023Alborova, M. S.; Vodop’yanov, S. K. 1 1992 Potential theory on homogeneous groups. Zbl 0695.31009Vodop’yanov, S. K. 2 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. 4 1989 Intrinsic geometries and boundary values of differentiable functions. I. Zbl 0692.46025Vodop’yanov, S. K. 2 1989 L\({}_ p\)-theory of potentials and quasi-conformal mappings on homogeneous groups. Zbl 0714.31005Vodop’yanov, S. K. 1 1989 Taylor’s formula and function spaces. Textbook. Zbl 0709.46009Vodop’yanov, S. K. 5 1988 Maximum principle in potential theory and imbedding theorems for anisotropic spaces of differentiable functions. Zbl 0699.31019Vodop’yanov, S. K. 2 1988 Equivalent normalizations of Sobolev and Nikol’skiĭ spaces in domains. Boundary values and extension. Zbl 0646.46028Vodop’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 Prolongement des fonctions de classe \(R^ n\) et applications quasi conformes. Zbl 0451.30014Gol’dstein, Vladimir Mikailovitch; Vodop’janov, Sergei Konstantinovitch 5 1980 On geometric properties of functions with generalized first derivatives. Zbl 0429.30017Vodop’yanov, S. K.; Gol’dshteĭn, V. M.; Reshetnyak, Yu. G. 12 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. 11 1979 Quasiconformal mappings and spaces of functions with generalized first derivatives. Zbl 0353.30019Vodop’yanov, S. K.; Gol’dshtejn, V. M. 24 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 Functional characteristics of quasiisometric mappings. Zbl 0389.30014Vodop’yanov, S. K.; Gol’dshtejn, V. M. 6 1977 Functional characteristics of quasi-isometric mappings. Zbl 0364.30030Vodop’yanov, S. K.; Gol’dshtejn, V. M. 1 1976 Lattice isomorphisms of the spaces \(W^1_n\) and quasiconformal mappings. Zbl 0324.46040Vodop’yanov, S. K.; Gol’dshtejn, V. M. 13 1975 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 Estimates of the deviation from a sphere of quasiumbilical surfaces. Zbl 0214.49205Vodop’yanov, S. K. 1 1971 all cited Publications top 5 cited Publications all top 5 Cited by 186 Authors 50 Karmanova, Maria B. 43 Vodop’yanov, Sergeĭ Konstantinovich 21 Ukhlov, Alexander Dadar-Oolovich 20 Gol’dshtein, Vladimir Mikhailovich 10 Ryazanov, Vladimir Il’ich 9 Evseev, Nikita Aleksandrovich 8 Sevost’yanov, Yevgen Oleksandrovych 7 Isangulova, D. V. 7 Koskela, Pekka 7 Salimov, Ruslan Radikovich 6 Markina, Irina 6 Selivanova, Svetlana V. 5 Basalaev, S. G. 5 Greshnov, Aleksandr Valer’evich 5 Molchanova, Anastasia Olegovna 5 Morbidelli, Daniele 5 Pchelintsev, Valerii 5 Tryamkin, Maksim Vladimirovich 4 Gutlyanskiĭ, Vladimir Ya. 4 Kovtonyuk, D. A. 4 Menovshchikov, A. V. 4 Zhou, Yuan 3 Dymchenko, Yuriĭ Viktorovich 3 Garofalo, Nicola 3 Monti, Roberto 3 Shvartsman, Pavel 3 Troyanov, Marc 3 Zobin, Nahum 2 Battaglia, Erika 2 Bevan, Jonathan J. 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 Karmanova, M. V. 2 Kleprlík, Luděk 2 Kudryavtseva, N. A. 2 Lomako, Tetiana 2 Menovschikov, Alexander 2 Montanari, Annamaria 2 Montefalcone, Francescopaolo 2 Müller, Stefan 2 Nhieu, Duy-Minh 2 Passarelli di Napoli, Antonia 2 Peltonen, Kirsi 2 Rajala, Kai 2 Rajala, Tapio 2 Serra Cassano, Francesco 2 Soto, Tomás 2 Spector, Scott J. 2 Tyulenev, A. I. 2 Zürcher, Thomas 1 Achdou, Yves 1 Adamowicz, Tomasz 1 Alborova, M. S. 1 Ambrosio, Luigi 1 Arutyunov, Aram Vladimirovic 1 Asaki, Thomas J. 1 Ball, John M. 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 Brakalova, Melkana Aleksandrova 1 Bramanti, Marco 1 Brandolini, Luca 1 Brewster, Kevin 1 Bukhvalov, Alexander V. 1 Buliga, Marius G. 1 Chahbi, Abdellatif 1 Charifi, Ahmed 1 Chebanenko, Nikita Alekseevich 1 Christ, Michael 1 Ciarlet, Philippe Gaston 1 Cinti, Eleonora 1 Cowling, Michael G. 1 Dambrine, Marc 1 Danielli, Donatella 1 De Cicco, Virginia 1 Egorov, Aleksandr Anatol’evich 1 Farroni, Fernando 1 Filatov, V. V. 1 Gaczkowski, Michał 1 Gamara, Najoua 1 Giannetti, Flavia 1 Giova, Raffaella 1 González, María del Mar 1 Górka, Przemysław 1 Guerra, André 1 Güneysu, Batu 1 Gurov, L. G. ...and 86 more Authors all top 5 Cited in 74 Serials 57 Siberian Mathematical Journal 43 Doklady Mathematics 13 Journal of Mathematical Sciences (New York) 11 Journal of Mathematical Analysis and Applications 8 Mathematical Notes 8 Journal of Functional Analysis 7 The Journal of Geometric Analysis 6 Russian Mathematics 6 St. Petersburg Mathematical Journal 5 Archive for Rational Mechanics and Analysis 5 Journal d’Analyse Mathématique 5 Advances in Mathematics 5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 Calculus of Variations and Partial Differential Equations 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 Variables and Elliptic Equations 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 Mathematische Zeitschrift 2 Proceedings of the American Mathematical Society 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Geometric and Functional Analysis. GAFA 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Izvestiya: Mathematics 2 Lobachevskii Journal of Mathematics 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 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 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 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Georgian Mathematical Journal 1 Sbornik: Mathematics 1 The Journal of Fourier Analysis and Applications 1 Annales Academiae Scientiarum Fennicae. Mathematica 1 Abstract and Applied Analysis 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 all top 5 Cited in 28 Fields 96 Functions of a complex variable (30-XX) 85 Differential geometry (53-XX) 84 Functional analysis (46-XX) 45 Partial differential equations (35-XX) 31 Calculus of variations and optimal control; optimization (49-XX) 21 Real functions (26-XX) 21 Global analysis, analysis on manifolds (58-XX) 18 Operator theory (47-XX) 16 Topological groups, Lie groups (22-XX) 16 Abstract harmonic analysis (43-XX) 13 Potential theory (31-XX) 10 Mechanics of deformable solids (74-XX) 9 Measure and integration (28-XX) 7 General topology (54-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 5 Geometry (51-XX) 4 Combinatorics (05-XX) 3 Several complex variables and analytic spaces (32-XX) 2 Nonassociative rings and algebras (17-XX) 2 Convex and discrete geometry (52-XX) 2 Manifolds and cell complexes (57-XX) 1 Mathematical logic and foundations (03-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 Numerical analysis (65-XX) 1 Quantum theory (81-XX) 1 Systems theory; control (93-XX) Citations by Year