Curvature integrals under the Ricci flow on surfaces |
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Authors: | Takumi Yokota |
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Institution: | (1) Graduate School of Pure and Applied Sciences, University of Tsukuba, 305-8571 Tsukuba, Japan |
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Abstract: | In this paper, we consider the behavior of the total absolute and the total curvature under the Ricci flow on complete surfaces
with bounded curvature. It is shown that they are monotone non-increasing and constant in time, respectively, if they exist
and are finite at the initial time. As a related result, we prove that the asymptotic volume ratio is constant under the Ricci
flow with non-negative Ricci curvature, at the end of the paper.
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Keywords: | Ricci flow Total absolute curvature Total curvature Asymptotic volume ratio |
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