Affine Bernstein problems and Monge-Ampère equations /

Affine Bernstein problems and Monge-Ampère equations /

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Bibliographic Details
Imprint:	New Jersey : World Scientific, ©2010.
Description:	1 online resource (xii, 180 pages) : illustrations
Language:	English
Subject:	Affine differential geometry. Monge-Ampère equations. Affine differential geometry. Monge-Ampère equations. Electronic books.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11284577

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Other authors / contributors:	Li, An-Min, 1946-
ISBN:	9789812814173 9812814175 9789812814166 9812814167
Notes:	Includes bibliographical references (pages 173-177) and index. Print version record.
Summary:	In this monograph, the interplay between geometry and partial differential equations (PDEs) is of particular interest. It is well-known that many geometric problems in analytic formulation lead to important classes of PDEs. The focus of this monograph is on variational problems and higher order PDEs for affine hypersurfaces. Affine maximal hypersurfaces are extremals of the interior variation of the affinely invariant volume. The corresponding Euler-Lagrange equation is a highly complicated nonlinear fourth order PDE. In recent years, the global study of such fourth order PDEs has received con.
Other form:	Print version: Affine Bernstein problems and Monge-Ampère equations. Singapore ; Hackensack, NJ : World Scientific, ©2010 9789812814166

Description
Summary:	In this monograph, the interplay between geometry and partial differential equations (PDEs) is of particular interest. It gives a selfcontained introduction to research in the last decade concerning global problems in the theory of submanifolds, leading to some types of Monge-Amp#65533;re equations.From the methodical point of view, it introduces the solution of certain Monge-Amp#65533;re equations via geometric modeling techniques. Here geometric modeling means the appropriate choice of a normalization and its induced geometry on a hypersurface defined by a local strongly convex global graph. For a better understanding of the modeling techniques, the authors give a selfcontained summary of relative hypersurface theory, they derive important PDEs (e.g. affine spheres, affine maximal surfaces, and the affine constant mean curvature equation). Concerning modeling techniques, emphasis is on carefully structured proofs and exemplary comparisons between different modelings.
Physical Description:	1 online resource (xii, 180 pages) : illustrations
Bibliography:	Includes bibliographical references (pages 173-177) and index.
ISBN:	9789812814173 9812814175 9789812814166 9812814167