Curvature integrals under the Ricci flow on surfaces

Takumi Yokota

doi:10.1007/s10711-008-9241-5

Curvature integrals under the Ricci flow on surfaces

Takumi Yokota

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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.

Original language	English
Pages (from-to)	169-179
Number of pages	11
Journal	Geometriae Dedicata
Volume	133
Issue number	1
DOIs	https://doi.org/10.1007/s10711-008-9241-5
Publication status	Published - 2008 Apr

Keywords

Asymptotic volume ratio
Ricci flow
Total absolute curvature
Total curvature

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10.1007/s10711-008-9241-5

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keywords = "Asymptotic volume ratio, Ricci flow, Total absolute curvature, Total curvature",

author = "Takumi Yokota",

note = "Funding Information: Acknowledgments The author would like to express his gratitude to Professor Takao Yamaguchi for his constant advice and suggestions. The author is also grateful to Professor Satoshi Ishiwata for numerous stimulating discussions. This work was partially supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists.",

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AU - Yokota, Takumi

N1 - Funding Information: Acknowledgments The author would like to express his gratitude to Professor Takao Yamaguchi for his constant advice and suggestions. The author is also grateful to Professor Satoshi Ishiwata for numerous stimulating discussions. This work was partially supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists.

PY - 2008/4

Y1 - 2008/4

N2 - 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.

AB - 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.

KW - Asymptotic volume ratio

KW - Ricci flow

KW - Total absolute curvature

KW - Total curvature

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JO - Geometriae Dedicata

JF - Geometriae Dedicata

IS - 1

ER -

Curvature integrals under the Ricci flow on surfaces

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Keywords

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