Acta mathematica scientia, Series B >
THE SURFACE AREA PRESERVING MEAN CURVATURE FLOW IN QUASI-FUCHSIAN MANIFOLDS
Received date: 2011-06-20
Online published: 2012-11-20
Supported by
The research is partially supported by NSFC (10971055, 11171096), RFDP (20104208110002), Funds for Disciplines Leaders of Wuhan (Z201051730002) and the Scientific Research Project of Jianghan University (2011017).
In this paper, we consider the surface area preserving mean curvature flow in quasi-Fuchsian 3-manifolds. We show that the flow exists for all times and converges exponentially to a smooth surface of constant mean curvature with the same surface area as the initial surface.
Key words： quasi-Fuchsian 3-manifold; parabolic equation; maximum principle
TIAN Da-Ping , LI Guang-Han , WU Chuan-Xi . THE SURFACE AREA PRESERVING MEAN CURVATURE FLOW IN QUASI-FUCHSIAN MANIFOLDS[J]. Acta mathematica scientia, Series B, 2012 , 32(6) : 2191 -2202 . DOI: 10.1016/S0252-9602(12)60169-6
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