Curvature Problems

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.