Geometry and Topology Seminar: On the Existence of Convex Surfaces with Prescribed k-Symmetric Curvatures.
12 November 2015 13:00 in CM221
The classification of surfaces with given curvature conditions is a fundamental question in differential geometry. The Minkowski problem and its solution (Minkowski, Niremberg, Pogorelov, Cheng-Yau and others) by means of analytic methods led to the development of the theory of Monge-Ampere equations. This has inspired others to address the same question for mean and scalar curvatures, which are particular cases of k-symmetric curvatures. We give an overview of investigations on the existence of the solution of this problem initiated by the work of B. Guan and P. Guan.