Curvature Problems (Series in Geometry and Topology)

Gerhardt, Claus

International Press of Boston Inc（2007/09発売）

• 製本 Hardcover:ハードカバー版／ページ数 323 p.
• 言語 ENG
• 商品コード 9781571461629

Full Description

Applying analytic methods to geometric problems has proved to be extremely fruitful in the last decades. Among the new techniques, with the help of which many problems have been solved, curvature flows and a priori estimates for fully non-linear elliptic partial differential equations are especially important. In this book, the author considers curvature problems in Reimannian and Lorentzian geometry which have in common either that the extrinsic curvature of closed hypersurfaces is prescribed or that curvature flows driven by the extrinsic curvature are studied and used to obtain some insight in the nature of possible singularities. This book will serve as an advanced textbook for graduate students and researchers interested in geometry and general relativity.

Contents

* Click here to view the Preface and Table of Contents as a PDF file; 1. Foundations; 2. Curvature flows in semi-Riemannian manifolds; 3. Hypersurfaces of prescribed curvature in Riemannian manifolds; 4. Hypersurfaces of prescribed curvature in Lorentzian manifolds; 5. Hypersurfaces of prescribed scalar curvature; 6. The IMCF in cosmological spacetimes.