By An-Min Li, Ruiwei Xu, Udo Simon, Fang Jia

ISBN-10: 9812814167

ISBN-13: 9789812814166

During this monograph, the interaction among geometry and partial differential equations (PDEs) is of specific curiosity. It provides a selfcontained advent to investigate within the final decade relating international difficulties within the concept of submanifolds, resulting in a few forms of Monge-AmpÃ¨re equations. From the methodical viewpoint, it introduces the answer of sure Monge-AmpÃ¨re equations through geometric modeling suggestions. right here geometric modeling capacity the best number of a normalization and its brought about geometry on a hypersurface outlined by means of an area strongly convex international graph. For a greater figuring out of the modeling recommendations, the authors supply a selfcontained precis of relative hypersurface thought, they derive very important PDEs (e.g. affine spheres, affine maximal surfaces, and the affine consistent suggest curvature equation). referring to modeling recommendations, emphasis is on rigorously dependent proofs and exemplary comparisons among varied modelings.