Affine Bernstein problems and Monge-Ampère equations / An-Min Li ... [et al.].

Format:

Book

Contributor:

Li, An-Min, 1946-

Language:

English

Subjects (All):

Affine differential geometry.

Monge-Ampère equations.

Physical Description:

1 online resource (192 p.)

Edition:

1st ed.

Place of Publication:

Singapore ; Hackensack, N.J. : World Scientific, c2010.

Language Note:

English

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

Contents:

Preface; Contents; 1. Basic Tools; 2. Local Equiaffine Hypersurfaces; 3. Local Relative Hypersurfaces; 4. The Theorem of Jorgens-Calabi-Pogorelov; 5. Affine Maximal Hypersurfaces; 6. Hypersurfaces with Constant Affine Mean Curvature; Bibliography; Index

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 173-177) and index.

ISBN:

9786612760280

9781282760288

1282760289

9789812814173

9812814175

OCLC:

670429445