Surfaces expanding by the power of the Gauss curvature flow
Author:
QiRui Li
Journal:
Proc. Amer. Math. Soc. 138 (2010), 40894102
MSC (2010):
Primary 53C44, 35K55
Published electronically:
June 16, 2010
MathSciNet review:
2679630
Fulltext PDF Free Access
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Abstract: In this paper, we describe the flow of 2surfaces 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 2dimensional 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
QiRui Li
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou 310027, People’s Republic of China
Email:
85lqr@163.com
DOI:
http://dx.doi.org/10.1090/S000299392010104318
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.
