PreprintCC BY 4.0arXiv
An L1 bound for Ricci curvature on Kähler manifolds
Abstract
We prove a uniform L1 bound for Ricci curvature on noncollapsed Kähler manifolds with Ricci curvature bounded below. The proof combines the codimension two neck decomposition and entropy estimates with local Kähler geometry on regular balls. The key step is a linear control of the Ricci integral on a regular ball by the entropy pinching, obtained from a decomposition of the scalar-curvature integral that exploits the Kähler structure.
Related
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BibTeX
@misc{jiang2026bound,
title = {{An $L^1$ bound for Ricci curvature on Kähler manifolds}},
author = {Wenshuai Jiang and Gang Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28142},
eprint = {2610.28142},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28142},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An L^1 bound for Ricci curvature on Kähler manifolds
AU - Wenshuai Jiang
AU - Gang Liu
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28142
UR - https://arxiv.org/abs/2610.28142
AB - We prove a uniform L^1 bound for Ricci curvature on noncollapsed Kähler manifolds with Ricci curvature bounded below. The proof combines the codimension two neck decomposition and entropy estimates with local Kähler geometry on regular balls. The key step is a linear control of the Ricci integral on a regular ball by the entropy pinching, obtained from a decomposition of the scalar-curvature integral that exploits the Kähler structure.
ER -