Compactness of Constant Mean Curvature Surfaces in Three Manifold with Positive Ricci Curvature

Abstract

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

20 pages. Fix a mistake in the main theorem and the application (I want to thank Jonathan Zhu for pointing it out). Comments are welcomed!