Constant mean curvature foliation: singularity structure and curvature estimate

Rugang Ye

Vol. 174 (1996), No. 2, 569–587

DOI: 10.2140/pjm.1996.174.569

Abstract

We study constant mean curvature foliations with isolated center singularities in 3-dimensions. We prove that the leaves become round upon approaching a center. We also derive a priori curvature estimates for constant mean curvature foliations without stability condition. A complete existence, uniqueness and non-existence result for constant mean curvature foliations around a center is derived as a consequence. These results are extended to constant mean curvature foliations on asymptotically flat ends.

Mathematical Subject Classification 2000

Primary: 53C12

Secondary: 53A10

Milestones

Received: 7 December 1993

Revised: 28 August 1995

Published: 1 June 1996