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Removing scalar curvature assumption for Ricci flow smoothing
- Publication Year :
- 2024
-
Abstract
- In recent work of Chan-Huang-Lee, it is shown that if a manifold enjoys uniform bounds on (a) the negative part of the scalar curvature, (b) the local entropy, and (c) volume ratios up to a fixed scale, then there exists a Ricci flow for some definite time with estimates on the solution assuming that the local curvature concentration is small enough initially (depending only on these a priori bounds). In this work, we show that the bound on scalar curvature assumption (a) is redundant. We also give some applications of this quantitative short-time existence, including a Ricci flow smoothing result for measure space limits, a Gromov-Hausdorff compactness result, and a topoligical and geometric rigidity result in the case that the a priori local bounds are strengthened to be global.<br />Comment: 19 pages
- Subjects :
- Mathematics - Differential Geometry
53E20
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2408.11115
- Document Type :
- Working Paper