arXiv:1105.3150 Abstract | arXiv Analytics

arXiv:1105.3150 [math.DG]Abstract References Reviews Resources

The space of Constant Mean Curvature surfaces in compact Riemannian Manifolds

Published 2011-05-16, updated 2011-08-29Version 3

The main point of this paper is that, under suitable conditions on the mean curvature and the Ricci curvature of the ambient space, we can extend Choi-Schoen's Compactness Theorem to compact embedded minimal surfaces to simple immersed compact H-surfaces in a Riemannian manifold with positive Ricci curvature (the mean curvature small depending on the Ricci curvature). Also, we prove that the space of convex embedded (fixed) constant mean curvature hypersurfaces in a simply connected 1/4-pinched manifold is compact.

Comments: The paper have been withdrawn since the cornerstone area estimate (Theorem 2.1 Ho, Pak Tung, "A first eigenvalue estimate for embedded hypersurfaces". Differential Geom. Appl. 26 (2008), no. 3, 273-276.) does not look right. Therefore, the author has decided to withdraw the paper

Categories: math.DG

Subjects: 53A10, 53C21, 47H11

Keywords: constant mean curvature surfaces, compact riemannian manifolds, ricci curvature, constant mean curvature hypersurfaces, extend choi-schoens compactness theorem

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