In: The Journal of Geometric Analysis, 2020, p. -
We discuss the links between stationary discs, the defect of analytic discs, and 2-jet determination of CR automorphisms of generic nondegenerate real submanifolds of CN of class C4.
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In: Advances in Mathematics, 2019, vol. 343, p. 910–934
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In: Proceedings of the American Mathematical Society, 2016, p. -
We study nonlinear automorphisms of Levi degenerate hypersurfaces of finite multitype. By results of Kolar, Meylan, and Zaitsev in 2014, the Lie algebra of infinitesimal CR automorphisms may contain a graded component consisting of nonlinear vector fields of arbitrarily high degree, which has no analog in the classical Levi nondegenerate case, or in the case of finite type hypersurfaces in $ ...
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In: Advances in Mathematics, 2014, vol. 263, p. 321–356
We consider the fundamental invariant of a real hypersurface in CN – its holomorphic symmetry group – and analyze its structure at a point of degenerate Levi form. Generalizing the Chern–Moser operator to hypersurfaces of finite multitype, we compute the Lie algebra of infinitesimal symmetries of the model and provide explicit description for each graded component. Compared with...
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In: Communications in Partial Differential Equations, 2008, vol. 33, no. 9, p. 1638 - 1653
The Schwarz reflection principle in one complex variable can be stated as follows. Let M and M' be two real analytic curves in ℂ and f a holomorphic function defined on one side of M, extending continuously through M, and mapping M into M'. Then f has a holomorphic extension across M. In this paper, we extend this classical theorem...
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In: Proceedings of the American Mathematical Society, 2006, vol. 134, p. 1023-1030
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