Acta mathematica scientia,Series B ›› 2012, Vol. 32 ›› Issue (6): 2191-2202.doi: 10.1016/S0252-9602(12)60169-6

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THE SURFACE AREA PRESERVING MEAN CURVATURE FLOW IN QUASI-FUCHSIAN MANIFOLDS

 TIAN Da-Ping1, LI Guang-Han2, WU Chuan-Xi3*   

  1. 1.School of Mathematics and Computer Science, Jianghan University, Wuhan 430056, China; 2.School of Mathematics and Computer Science, Hubei University, Wuhan 430062, China; 3.School of Mathematics and Computer Science, Key Laboratory of Applied Mathematics of Hubei Province, Hubei University, Wuhan 430062, China
  • Received:2011-06-20 Online:2012-11-20 Published:2012-11-20
  • Contact: WU Chuan-Xi,cxwu@hubu.edu.cn E-mail:tdp761128@163.com;liguanghan@163.com;cxwu@hubu.edu.cn
  • 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).

Abstract:

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

CLC Number: 

  • 53C44
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