Bounds on volume growth of geodesic balls under Ricci flow

Qi S. Zhang

Bounds on volume growth of geodesic balls under Ricci flow

Differential Geometry 2011-10-11 v2 Analysis of PDEs

Authors: Qi S. Zhang

Abstract

We prove a so called $\kappa$ non-inflating property for Ricci flow, which provides an upper bound for volume ratio of geodesic balls over Euclidean ones, under an upper bound for scalar curvature. This result can be regarded as the opposite statement of Perelman's $\kappa$ non-collapsing property for Ricci flow. These two results together imply volume doubling property for Ricci flow without assuming Ricci curvature lower bound.

Keywords

Ricci flow volume growth geodesic ball kappa non-inflating property scalar curvature volume doubling property

Cite

@article{arxiv.1107.4262,
  title  = {Bounds on volume growth of geodesic balls under Ricci flow},
  author = {Qi S. Zhang},
  journal= {arXiv preprint arXiv:1107.4262},
  year   = {2011}
}

Comments

One reference on related result [CW2] added. A typo at last line of p3 corrected. The last coefficient p(t) in the line should be in front of \Delta u only

Bounds on volume growth of geodesic balls under Ricci flow

Abstract

Keywords

Cite

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