Compactness of constant mean curvature surfaces in a three-manifold with positive Ricci curvature

Ao Sun

Vol. 305 (2020), No. 2, 735–756

DOI: 10.2140/pjm.2020.305.735

Abstract

We prove a compactness theorem for constant mean curvature surfaces with area and genus bound in a three-manifold with positive Ricci curvature. As an application, we give a lower bound of the first eigenvalue of constant mean curvature surfaces in a three-manifold with positive Ricci curvature.

Keywords

constant mean curvature surfaces, compactness

Mathematical Subject Classification 2010

Primary: 53A10, 58C40

Milestones

Received: 2 May 2018

Revised: 10 February 2019

Accepted: 11 October 2019

Published: 29 April 2020