Affine Bernstein Problems And Monge-ampere Equations
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A01=An-min Li
A01=Fang Jia
A01=Ruiwei Xu
A01=Udo Simon
Affine Bernstein Problems
Affine Hyperspheres
Affine Maximal Hypersurfaces
Author_An-min Li
Author_Fang Jia
Author_Ruiwei Xu
Author_Udo Simon
Blaschke Hypersurface
Calabi Metric
Category=PBKJ
Category=PBM
Completeness in Affine Hypersurface Theory
Constant Affine Mean Curvature Equation
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Geometric Modeling of PDEs
Monge-AmpAfA?re Equations
Monge-Ampere Equations
Monge-Ampère Equations
Relative Hypersurface Theory
Product details
- ISBN 9789812814166
- Publication Date: 28 Apr 2010
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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-Ampère equations.From the methodical point of view, it introduces the solution of certain Monge-Ampère 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.
