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- Publisher
- Springer Journals
- Copyright
- Copyright © Mathematica Josephina, Inc. 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
- ISSN
- 1050-6926
- eISSN
- 1559-002X
- DOI
- 10.1007/s12220-022-01017-8
- Publisher site
- See Article on Publisher Site
Abstract
In this short survey article, we mention some of Peter Li’s tremendous influence on geometric analysis, focusing on the development of Li–Yau inequalities and related ideas in geometric analysis and geometric flows. This started with the seminal 1986 Li–Yau paper, Hamilton’s development for geometric flows, and in particular his miraculous matrix Harnack estimate for the Ricci flow, Perelman’s differential Harnack estimate for the conjugate heat kernel under a Ricci flow background, and his related monotonicity formulas for Ricci flow, and Bamler’s recent sharp gradient estimates, new monotonicity formulas, and their applications for Ricci flow.
Journal
The Journal of Geometric Analysis – Springer Journals
Published: Nov 1, 2022
Keywords: Li–Yau inequality; Differential Harnack estimate; Gradient estimate; 53E20; 53E10; 58J35; 58J05