The space of Constant Mean Curvature surfaces in compact Riemannian Manifolds

Details The space of Constant Mean Curvature surfaces in compact Riemannian Manifolds The space of Constant Mean Curvature surfaces in compact Riemannian Manifolds

2011-05-16

arxiv.org/abs/1105.3150v3

Mathematics

Differential Geometry

The paper have been withdrawn since the cornerstone area estimate (Theorem 2.1 Ho, Pak Tung, "A first eigenvalue estimate for

Scientific paper

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.

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