Research Interests of Dmitri Zaitsev
Several Complex Variables:
- Normal forms of real submanifolds in complex spaces
- Proper holomorphic mappings and correspondences
- Rigidity of proper and CR maps
- Bounded symmetric domains
- Meromorphic and bimeromorphic mappings
- Automorphism groups of complex spaces
- Semi-analytic and sub-analytic sets
- CR manifolds
- Holomorphic foliations and webs
Real and Complex Algebraic Geometry:
- Algebraic and analytic cycle spaces
- Real algebraic and semialgebraic sets
- Nash functions and manifolds
Symplectic Geometry and Lie Group actions
Selected Papers:
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Kolar, M.; Meylan, F.; Zaitsev, D. --- Chern-Moser operators and polynomial models in CR geometry.
Advances in Mathematics 263 (2014), no. 2, 321-356.
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O'Farrell, A.G.; Zaitsev, D. --- Factoring formal maps into reversible or involutive factors.
Journal of Algebra 399 (2014), 657-674.
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Kim, S.Y.; Zaitsev, D. --- Rigidity of CR maps between Shilov boundaries
of bounded symmetric domains.
Inventiones Mathematicae 193 (2013), no. 2, 409-437.
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Dolbeault, P.; Tomassini, G.; Zaitsev, D. --- On Levi-flat hypersurfaces with prescribed boundary.
Pure and Applied Mathematics Quarterly
6 (2010), no. 3, Special Issue: In honor of Joseph J. Kohn. Part 1, 725-753.
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Baouendi, M.S.; Ebenfelt, P.; Zaitsev, D. --- A Cauchy-Kowalevsky theorem for overdetermined systems of nonlinear partial differential equations and geometric applications.
Communications in Partial Differential Equations 34 (2009), no. 10-12, 1180-1207.
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Lamel, B.; Mir, N.; Zaitsev, D. --- Lie group structures on automorphism groups of real-analytic CR manifolds.
American Journal of Mathematics
130 (2008), no. 6, 1709-1726.
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Zaitsev, D. --- Obstructions to embeddability into hyperquadrics and explicit examples.
Mathematische Annalen
342 (2008), no. 3, 695-726.
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Kim, S.-Y.; Zaitsev, D. --- Remarks on the rigidity of CR-manifolds.
Compositio Mathematica 142 (2006), no. 4, 1009-1017.
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Kim, S.-Y.; Zaitsev, D. --- Equivalence and embedding problems for CR-structures of any codimension.
Topology 44 (2005), no. 3, 557-584.
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Ebenfelt, P.; Huang, X.; Zaitsev, D.
--- The equivalence problem and rigidity for hypersurfaces embedded into hyperquadrics.
American Journal of Mathematics
127 (2005), no. 1, 169-191. PDF
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Baouendi, M.S.; Rothschild, L.P.; Winkelmann, J.; Zaitsev, D.
--- Lie group structures on groups of diffeomorphisms and applications to CR manifolds.
Annales de l'Institut Fourier (Grenoble)
54 (2004), no. 5, 1279-1303.
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Kaup, W.; Zaitsev, D.
--- On the CR-structure of compact group orbits associated with bounded symmetric domains.
Inventiones Mathematicae
153 (2003), no. 1, 45-104. PDF
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Zaitsev, D.; Zampieri, G. --- Extension of CR-functions on wedges.
Mathematische Annalen
326 (2003), no. 4, 691-703. PDF
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Ebenfelt, P.; Lamel, B.; Zaitsev, D.
--- Finite jet determination of local analytic CR automorphisms
and their parametrization by 2-jets in the finite type case.
Geometric and Functional Analysis
13 (2003), no. 3, 546-573. PDF
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Meylan, F.; Mir, N.; Zaitsev, D. --- Holomorphic extension of smooth CR-mappings between real-analytic and real-algebraic CR-manifolds.
The Asian Journal of Mathematics
7, (2003), no. 4, 493-509.
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Zaitsev, D. --- Unique determination of local CR-maps by their jets: A survey.
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Serie IX. Matematica e Applicazioni 13 (2002), 295-305.
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Zaitsev, D.
--- Algebraicity of local holomorphisms between real-algebraic submanifolds of complex spaces.
Acta Mathematica
183 (1999), 273-305.
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