Lower bounds for the scalar curvatures of Ricci flow singularity models-Reference-Cited by-同舟云学术

Lower bounds for the scalar curvatures of Ricci flow singularity models

Published:2022-12-15 Issue:0 Volume:0 Page:
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Chan Pak-Yeung¹,Chow Bennett¹,Ma Zilu²,Zhang Yongjia³^ORCID

Affiliation:

1. Department of Mathematics , University of California San Diego , La Jolla , CA 92093 , USA

2. Department of Mathematics , Rutgers University , Piscataway , NJ 08854 , USA

3. School of Mathematical Sciences , Shanghai Jiao Tong University , Minhang District , Shanghai , 200240 , P. R. China

Abstract

Abstract In a series of papers, Bamler [5, 4, 6] further developed the high-dimensional theory of Hamilton’s Ricci flow to include new monotonicity formulas, a completely general compactness theorem, and a long-sought partial regularity theory analogous to Cheeger–Colding theory. In this paper we give an application of his theory to lower bounds for the scalar curvatures of singularity models for Ricci flow. In the case of 4-dimensional non-Ricci-flat steady soliton singularity models, we obtain as a consequence a quadratic decay lower bound for the scalar curvature.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2022-0086/pdf

Reference38 articles.

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3. R. H. Bamler, Long-time behavior of 3-dimensional Ricci flow – Introduction, Geom. Topol. 22 (2018), no. 2, 757–774.

4. R. H. Bamler, Compactness theory of the space of super Ricci flows, preprint (2020), https://arxiv.org/abs/2008.09298.

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