Open Access
February, 2001 Mean Curvature Flow of Surfaces in Einstein Four-Manifolds
Mu-Tao Wang
J. Differential Geom. 57(2): 301-338 (February, 2001). DOI: 10.4310/jdg/1090348113


Let Σ be a compact oriented surface immersed in a four dimensional Kähler-Einstein manifold (M, w). We consider the evolution of Σ in the direction of its mean curvature vector. It is proved that being symplectic is preserved along the flow and the flow does not develop type I singularity. When M has two parallel Kähler forms w' and w" that determine different orientations and Σ is symplectic with respect to both w' and w", we prove the mean curvature flow of Σ exists smoothly for all time. In the positive curvature case, the flow indeed converges at infinity.


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Mu-Tao Wang. "Mean Curvature Flow of Surfaces in Einstein Four-Manifolds." J. Differential Geom. 57 (2) 301 - 338, February, 2001.


Published: February, 2001
First available in Project Euclid: 20 July 2004

zbMATH: 1035.53094
MathSciNet: MR1879229
Digital Object Identifier: 10.4310/jdg/1090348113

Rights: Copyright © 2001 Lehigh University

Vol.57 • No. 2 • February, 2001
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