Affine Berstein Problems and Monge-Ampere Equations - Couverture souple

Li, An-min

Couverture souple

ISBN 10 : 9812814167 ISBN 13 : 9789812814166

Editeur : World Scientific Publishing Company, 2010

Synopsis

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.

A propos du livre

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.

Biographie de l'auteur

The authors represent three generations of geometers. U Simon finished his doctoral thesis with K P Grotemeyer at the FU Berlin in 1965, and from his lectures he became interested in global differential geometry. U Simon became a professor of mathematics at TU Berlin in 1970. A M Li started his studies at Peking University in 1963, but because of the cultural revolution he could not finish his MS before 1982. Following a recommendation of S S Chern, he came as AvH fellow to the TU Berlin in 1986 the first time, and he finished his doctoral thesis there with U Simon, U Pinkall and K Nomizu. A M Li has been a professor of mathematics at Sichuan University since 1986, succesfully guiding research groups since then. A M Li was also the advisor of F Jia (PhD 1997) and R Xu (PhD 2008) at Sichuan University. Both are now professors themselves, F Jia at Sichuan University since 1997, R Xu at Henan Normal University since 2008.

Détails de l'édition

• Éditeur: World Scientific Publishing Company
• Date d'édition: 2010
• Langue: anglais
• ISBN 10: 9812814167
• ISBN 13: 9789812814166
• Reliure: Broché
• Nombre de pages: 192
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible