Vol. 305, No. 2, 2020

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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

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.

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constant mean curvature surfaces, compactness
Mathematical Subject Classification 2010
Primary: 53A10, 58C40
Received: 2 May 2018
Revised: 10 February 2019
Accepted: 11 October 2019
Published: 29 April 2020
Ao Sun
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States