Uniform Lipschitz Continuity of the Isoperimetric Profile of Compact Surfaces Under Normalized Ricci Flow

Author

Yizhong Zheng, The Graduate Center, City University of New YorkFollow

Date of Degree

6-2020

Document Type

Dissertation

Degree Name

Ph.D.

Program

Mathematics

Advisor

Bianca Santoro

Advisor

Hans-Joachim Hein

Committee Members

Dan Lee

Luis Fernandez

Subject Categories

Analysis | Geometry and Topology

Keywords

Ricci flow, isoperimetric profile

Abstract

We show that the isoperimetric profile h_{g(t)}(\xi) of a compact Riemannian manifold (M,g) is jointly continuous when metrics g(t) vary continuously. We also show that, when M is a compact surface and g(t) evolves under normalized Ricci flow, h^2_{g(t)}(\xi) is uniform Lipschitz continuous and hence h_{g(t)}(\xi) is uniform locally Lipschitz continuous.

Recommended Citation

Zheng, Yizhong, "Uniform Lipschitz Continuity of the Isoperimetric Profile of Compact Surfaces Under Normalized Ricci Flow" (2020). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/3767