Title: Boundary rigidity and filling minimality via the barycenter method
Speaker: Yuping Ruan
Speaker Info: University of Michigan, Ann Arbor
Special Note: The pre-seminar talk will be 3- 4 pm and the main talk will be 4 - 5 pm
A compact manifold with a smooth boundary is boundary rigid if its boundary and boundary distance function uniquely determine its interior up to boundary preserving isometries. Under certain natural conditions, the notion of boundary rigidity is closely related to Gromov's filling minimality. In this talk, we will give a brief overview of Burago-Ivanov's approach to prove filling minimality and boundary rigidity for almost Euclidean and almost real hyperbolic metrics. Then we will explain how we generalize their results to regions in a rank-1 symmetric space equipped with an almost symmetric metric. We will also explain the relations to Besson-Courtois-Gallot's barycenter constructions used in their celebrated volume entropy rigidity theorem.Date: Tuesday, January 24, 2023
Title: The barycenter method and its applications
Abstract: In this talk, we will focus on the barycenter construction introduced by Besson-Coutois-Gallot. We will first explain its application in their celebrated volume entropy rigidity theorem, which roughly states that ''symmetry implies minimal entropy''. If time permits, we will also mention some other applications, (e.g. bounded cohomology).