English

The sharp Li-Yau equality on Shrinking Ricci Solitons with applications

Differential Geometry 2020-09-22 v2

Abstract

We prove that the sharp Li-Yau equality holds for the conjugate heat kernel on shrinking Ricci solitons without any curvature or volume assumptions. This quantity yields several estimates which allows us to classify four dimensional, non-compact shrinking Ricci solitons, which arise as Type I singularity models to the Ricci flow.

Keywords

Cite

@article{arxiv.2009.06951,
  title  = {The sharp Li-Yau equality on Shrinking Ricci Solitons with applications},
  author = {Jason Ledwidge},
  journal= {arXiv preprint arXiv:2009.06951},
  year   = {2020}
}

Comments

17 pages. The first version claimed the classification was true in all dimensions. More information and results on the conjugate heat kernel given. Removal of asymptotic cone section from the previous version

R2 v1 2026-06-23T18:33:03.697Z