A Cauchy–Kowalevsky Theorem for Overdetermined Systems of Nonlinear Partial Differential Equations and Geometric Applications

DOI10.1080/03605300902910220zbMath1180.35379arXiv0811.1255OpenAlexW1972450446WikidataQ58623180 ScholiaQ58623180MaRDI QIDQ3653270

Peter Ebenfelt, Mohamed Salah Baouendi, Dimitri Zaitsev

Publication date: 22 December 2009

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0811.1255

zbMATH Keywords

Cauchy problemapproximate solutionsexterior differential systemsoverdetermined systemsfinitely nondegenerate hypersurfacesLevi number

Mathematics Subject Classification ID

Real submanifolds in complex manifolds (32V40) Cauchy-Kovalevskaya theorems (35A10) Exterior differential systems (Cartan theory) (58A15) Complex Monge-Ampère operators (32W20) Overdetermined systems of PDEs with variable coefficients (35N10) Finite-type conditions on CR manifolds (32V35) Overdetermined initial value problems for PDEs and systems of PDEs (35N20)

Cites Work

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• Classification of Levi degenerate homogeneous CR-manifolds in dimension 5
• Local biholomorphic straightening of real submanifolds
• Riquier's existence theorems
• Uniformly Levi degenerate CR manifolds: The 5-dimensional case
• Regularity of CR mappings between algebraic hypersurfaces
• Integrability criteria for systems of nonlinear partial differential equations
• On Spherical Image Maps Whose Jacobians Do Not Change Sign
• CR-manifolds of dimension 5: A Lie algebra approach
• COMPLETE DEVELOPABLE SUBMANIFOLDS IN REAL AND COMPLEX EUCLIDEAN SPACES
• On Hypersurfaces with no Negative Sectional Curvatures

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