Abstract:
The classical four vertex theorem characterizes an interesting property of closed planar curves. It has been extended to space curves on sphere and on more general convex surfaces, namely a smooth, closed curve in R^3 has at least four points with vanishing torsion if it lies on a convex surface. In this paper we discuss properties of locally convex surfaces and prove the existence of locally convex surfaces of constant Gauss curvature. As an application we prove the four vertex theorem for space curves on locally convex surfaces, extending the corresponding result of Ghomi.
Biography:
Xu-Jia Wang received his Ph.D. in mathematics from Zhejiang University in 1990. He was then a Lecturer and Associate Professor at Zhejiang University until 1995 when he moved to the Australian National University as a Research Fellow. He is currently a Professor of mathematics at the ANU. His research interest is analysis and partial differential equations, and their applications in geometry and physics.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai