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Backward Pseudolocality of G2-Laplacian Flow

  • Weiyong He
  • Longhuan Yan
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Abstract

In this paper, we establish a new estimate on the time-derivative of pointed Nash entropy and use it to give a new proof of backward pseudolocality for Ricci flow. The proof does not rely on Bamler's compactness theorem and structure theory concerning limits of Ricci flows. Our methods also work for other reasonable geometric flows, like the G2-Laplacian, at a scale depending on its deviation from Ricci flow and its scalar curvature.

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Cite

BibTeXRIS
BibTeX
@misc{he2026backward,
  title = {{Backward Pseudolocality of $G_2$-Laplacian Flow}},
  author = {Weiyong He and Longhuan Yan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38418},
  eprint = {2610.38418},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38418},
}
RIS
TY  - UNPB
TI  - Backward Pseudolocality of G_2-Laplacian Flow
AU  - Weiyong He
AU  - Longhuan Yan
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38418
UR  - https://arxiv.org/abs/2610.38418
AB  - In this paper, we establish a new estimate on the time-derivative of pointed Nash entropy and use it to give a new proof of backward pseudolocality for Ricci flow. The proof does not rely on Bamler's compactness theorem and structure theory concerning limits of Ricci flows. Our methods also work for other reasonable geometric flows, like the G_2-Laplacian, at a scale depending on its deviation from Ricci flow and its scalar curvature.
ER  -