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Some uniform estimates for Kähler--Ricci Shrinkers

  • Junsheng Zhang
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Abstract

In this paper, we establish several uniform estimates for Kähler--Ricci shrinkers without imposing any curvature assumptions. In particular, we prove: 1. a uniform lower bound for the entropy; 2. a uniform lower bound for the asymptotic volume ratio of Kähler--shrinkers with maximal volume growth; 3. a uniform lower bound for the scalar curvature on balls centered at a minimum point of the soliton potential for non-Gaussian shrinkers.

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Cite

BibTeXRIS
BibTeX
@misc{zhang2026some,
  title = {{Some uniform estimates for Kähler--Ricci Shrinkers}},
  author = {Junsheng Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.30779},
  eprint = {2608.30779},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30779},
}
RIS
TY  - UNPB
TI  - Some uniform estimates for Kähler--Ricci Shrinkers
AU  - Junsheng Zhang
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.30779
UR  - https://arxiv.org/abs/2608.30779
AB  - In this paper, we establish several uniform estimates for Kähler--Ricci shrinkers without imposing any curvature assumptions. In particular, we prove: 1. a uniform lower bound for the entropy; 2. a uniform lower bound for the asymptotic volume ratio of Kähler--shrinkers with maximal volume growth; 3. a uniform lower bound for the scalar curvature on balls centered at a minimum point of the soliton potential for non-Gaussian shrinkers.
ER  -