Diameter, Area, and Mean curvature

2024/12/05 by Chambers, Gregory R., Marx-Kuo, Jared
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.04636

Abstract

In this note, we extend diameter bounds of Simon, Topping, and Wu--Zheng to submanifolds with boundary and (potentially non-compact) ambient manifolds with minor curvature restrictions. The bound is dependent on both an integral of mean curvature and the area of the manifold. We apply our diameter bounds to minimal, constant mean curvature, and prescribed mean curvature surfaces arising in min-max constructions.

Related

• Diameter estimates for submanifolds in manifolds with nonnegative curvature
• Relating diameter and mean curvature for Riemannian submanifolds
• The sharp diameter bound of stable minimal surfaces
• Diameter estimates for surfaces in conformally flat spaces
• Surfaces of bounded mean curvature in Riemannian manifolds