Uniform Lipschitz continuity of the isoperimetric profile of compact surfaces under normalized Ricci flow

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, $h_{g(t)}^2(\xi )$ is uniform Lipschitz continuous and hence $h_{g(t)}(\xi )$ is uniform locally Lipschitz continuous.

17 pages; Made minor corrections to Theorem 1.2 and Corollary 1.3

References in corpus (3)

• Continuity of the isoperimetric profile of a complete Riemannian manifold under sectional curvature conditions
• A discontinuous isoperimetric profile for a complete Riemannian manifold
• On the Hamilton's isoperimetric ratio in complete Riemannian manifolds of finite volume