Surfaces expanding by the power of the Gauss curvature flow

Author:
Qi-Rui Li

Journal:
Proc. Amer. Math. Soc. **138** (2010), 4089-4102

MSC (2010):
Primary 53C44, 35K55

DOI:
https://doi.org/10.1090/S0002-9939-2010-10431-8

Published electronically:
June 16, 2010

MathSciNet review:
2679630

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we describe the flow of 2-surfaces in for some negative power of the Gauss curvature. We show that strictly convex surfaces expanding with normal velocity , when , 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 by Urbas and Huisken and for by Schnürer.

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Additional Information

**Qi-Rui Li**

Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou 310027, People’s Republic of China

Email:
85lqr@163.com

DOI:
https://doi.org/10.1090/S0002-9939-2010-10431-8

Keywords:
Surface,
expanding curvature flow,
velocity function $K^{-\alpha}$

Received by editor(s):
June 2, 2009

Received by editor(s) in revised form:
October 9, 2009, November 26, 2009, December 19, 2009, December 31, 2009, and February 6, 2010

Published electronically:
June 16, 2010

Communicated by:
Richard A. Wentworth

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.