Geometriae Dedicata

, Volume 133, Issue 1, pp 169–179

Curvature integrals under the Ricci flow on surfaces

Original Paper

DOI: 10.1007/s10711-008-9241-5

Cite this article as:
Yokota, T. Geom Dedicata (2008) 133: 169. doi:10.1007/s10711-008-9241-5

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.

Keywords

Ricci flowTotal absolute curvatureTotal curvature Asymptotic volume ratio

Mathematics Subject Classification (2000)

53C44

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Graduate School of Pure and Applied SciencesUniversity of TsukubaTsukubaJapan