Research-Complete Riemannian Manifolds and Sobolev Type Inequalities

Research

Geometry & Topology Seminar

Complete Riemannian Manifolds and Sobolev Type Inequalities

Speaker: Changyu Xia (Universidade de Braslia)
Time: Mar 18, 2021, 10:00-11:00
Location: Lecture Room 415, Block 3, Hui Yuan

Abstract

Understanding the structure of Riemannian manifolds is an important issue in differential geometry. Many interesting results about relations between curvature and topology of manifolds have appeared during the past years. In this talk, we'll introduce some results about complete open manifolds supporting a Sobolev type inequality. We'll see that complete open manifolds with nonnegative Ricci curvature on which some Sobolev type inequality holds are not very far from the Euclidean space and that Hadamard manifolds support many important inequalities.