Research Interests of Dmitri Zaitsev

Source: https://www.maths.tcd.ie/~zaitsev/research.html Parent: https://www.maths.tcd.ie/~zaitsev/

Research Interests of Dmitri Zaitsev

Several Complex Variables:

The shortest path between two truths \ in the real domain passes through the \ complex domain.

J. Hadamard

• 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

Check my arXiv.org list for the most recent papers and my publication list from MathSciNet

Selected Papers:

• Kolar, M.; Meylan, F.; Zaitsev, D. --- Chern-Moser operators and polynomial models in CR geometry. Advances in Mathematics 263 (2014), no. 2, 321-356. PDF

• O'Farrell, A.G.; Zaitsev, D. --- Formally reversible maps of C2. Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. (Serie V) 13 (2014), no. 2, 371-397. PDF

• O'Farrell, A.G.; Zaitsev, D. --- Factoring formal maps into reversible or involutive factors. Journal of Algebra 399 (2014), 657-674. PDF

• Kim, S.Y.; Zaitsev, D. --- Rigidity of CR maps between Shilov boundaries of bounded symmetric domains. Inventiones Mathematicae 193 (2013), no. 2, 409-437. PDF

• Bracci, F.; Zaitsev, D. --- Dynamics of one-resonant biholomorphisms. Journal of the European Mathematical Society (JEMS) 15 (2013), no. 1, 179-200. PDF

• Zaitsev, D. --- Normal forms for nonintegrable almost CR structures. American Journal of Mathematics 134 (2012), no. 4, 915-947. PDF

• Dolbeault, P.; Tomassini, G.; Zaitsev, D. --- Boundary problem for Levi flat graphs. Indiana University Mathematics Journal 60 (2011), no. 1, 161-170. PDF

• Zaitsev, D. --- Formal and finite order equivalences. Mathematische Zeitschrift 269 (2011), no. 3-4, 687-696. PDF

• 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. PDF

• 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. PDF

• 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. PDF

• Zaitsev, D. --- Obstructions to embeddability into hyperquadrics and explicit examples. Mathematische Annalen 342 (2008), no. 3, 695-726. PDF

• Zaitsev, D. --- On different notions of homogeneity for CR-manifolds. The Asian Journal of Mathematics 11 (2007), no. 2, 331-340. PDF

• Kim, S.-Y.; Zaitsev, D. --- Remarks on the rigidity of CR-manifolds. Compositio Mathematica 142 (2006), no. 4, 1009-1017. PDF

• Kaup, W.; Zaitsev, D. --- On local CR-transformations of Levi-degenerate group orbits in compact Hermitian symmetric spaces. Journal of the European Mathematical Society (JEMS) 8 (2006), no. 3, 465-490. PDF

• Kim, S.-Y.; Zaitsev, D. --- Equivalence and embedding problems for CR-structures of any codimension. Topology 44 (2005), no. 3, 557-584. PDF

• 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

• Ebenfelt, P.; Huang, X.; Zaitsev, D. --- Rigidity of CR-immersions into spheres. Communications in Analysis and Geometry 12 (2004), no. 3, 631-670. PDF

• 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. PDF

• Kaup, W.; Zaitsev, D. --- Non-embeddable CR-manifolds of higher codimension. Journal für die Reine und Angewandte Mathematik (Crelle's Journal) 569 (2004), 1-12. PDF

• Zaitsev, D.; Zampieri, G. --- Extension of CR-functions into weighted wedges through families of nonsmooth analytic discs. Transactions of the American Mathematical Society 356 (2004), no. 4, 1443-1462. PDF

• 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

• Zaitsev, D.; Zampieri, G. --- Extension of CR-functions on wedges. Mathematische Annalen 326 (2003), no. 4, 691-703. PDF

• 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

• 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. PDF

• Meylan, F.; Mir, N.; Zaitsev, D. --- Approximation and convergence of formal CR-mappings. International Mathematics Research Notices 2003, no. 4, 211-242. PDF

• Hayashimoto, A.; Kim, S.-Y.; Zaitsev, D. --- Decomposition of CR-manifolds and splitting of CR-maps. Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. (Serie V) 2 (2003), no. 3, 433-448. PDF

• 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. PDF

• Meylan, F.; Mir, N.; Zaitsev, D. --- Analytic regularity of CR-mappings. Mathematical Research Letters 9 (2002), no. 1, 73-93. PDF

• Baouendi, M.S.; Rothschild, L.P.; Zaitsev, D. --- Equivalences of real submanifolds in complex space. Journal of Differential Geometry 59 (2001), no. 2, 301-351. PDF

• Kaup, W.; Zaitsev, D. --- On symmetric Cauchy-Riemann manifolds. Advances in Mathematics 149 (2000), no. 2, 145-181. PDF

• Zaitsev, D. --- Algebraicity of local holomorphisms between real-algebraic submanifolds of complex spaces. Acta Mathematica 183 (1999), 273-305. PDF

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