Surfaces expanding by the power of the Gauss curvature flow
- Autores: Qi-Rui Li
- Localización: Proceedings of the American Mathematical Society, ISSN 0002-9939, Vol. 138, Nº 11, 2010, págs. 4089-4102
- Idioma: inglés
- DOI: 10.1090/s0002-9939-2010-10431-8
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Resumen
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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