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

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

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.

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Bibliographische Detailangaben
Veröffentlicht in:Acta mathematica scientia 2012-11, Vol.32 (6), p.2191-2202
1. Verfasser: 田大平 李光汉 吴传喜
Format: Artikel
Sprache:eng
Schlagworte:
35K55
53A35
53C44
Curvature
Manifolds
Mathematical analysis
maximum principle
parabolic equation
Preserving
quasi-Fuchsian 3-manifold
Surface area
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Beschreibung
Zusammenfassung: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.
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(12)60169-6