Abstract:
In this talk, we first introduce some basic definitions such as horizontal objects, the Carnot-Caratheodory distance and graded vector spaces in sub-Riemannian manifolds. We further talk about Chow’s connectivity theorem, Hausdorff dimension theorem (Mitchell(85’), Pansu(89’)) and nilpotentization etc. Finally we discuss sub-geodesics in sub-Riemannian manifolds. Actually we also describe some motivations and backgrounds of sub-Riemannian manifolds with emphasizing the intrinsic differences between sub-Riemannian and Riemannian geometries.
Biography:
Xiaoping Yang received his Ph.D. in mathematics in 1992 from Hunan University, China. He worked as a Professor at School of Science, Nanjing University of Science and Technology, China from 1998 to 2015. From 2016, he is a Professor at Department of Mathematics, Nanjing University. His research interests include geometric measure theory, partial differential equations and their applications.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai