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ISSN 1088-6826(e) ISSN 0002-9939(p)

Surfaces expanding by the power of the Gauss curvature flow

Author(s): Qi-Rui Li
Journal: Proc. Amer. Math. Soc. 138 (2010), 4089-4102.
MSC (2010): Primary 53C44, 35K55
Posted: June 16, 2010
MathSciNet review: 2679630
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: In this paper, we describe the flow of 2-surfaces in $\mathbb{R}^{3}$ for some negative power of the Gauss curvature. We show that strictly convex surfaces expanding with normal velocity $K^{-\alpha }$ , when $\frac{1}{2}<\alpha \leq 1$ , converge to infinity in finite time. After appropriate rescaling, they converge to spheres. In the 2-dimensional case, our results close an apparent gap in the powers considered by previous authors, that is, for $\alpha \in (0,\frac{1}{2}]$ by Urbas and Huisken and for $\alpha =1$ by Schnürer.

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