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AFFINE MAXIMAL HYPERSURFACES
by An-Min Li, Fang Jia (Sichuan University, China) & Udo Simon (Technische Universität Berlin, Germany)
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 considerable attention. The authors, leading experts in the field with strong own contributions, present a systematic exposition of the topics in this book.
Contents:
- Local Equiaffine Hypersurface Theory
- Pogorelov’s Theorem
- Affine
Maximal Hypersurfaces
Readership: Advanced undergraduate and graduate students in mathematics;
researchers in global differential geometry, affine differential geometry and higher order PDEs.
| 200pp (approx.) |
Pub. date: Scheduled Winter 2008 |
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