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arXiv · 2604.17367

Weighted volume comparison and monotonicity for $L^p$-bound of Bakry-\'{E}mery Ricci curvature

Jintao Ye·Xiaohua Zhu
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Abstract

We establish a Petersen-Wei type relative volume comparison theorem for weighted Riemannian manifolds under both $L^p$-bounds of the Bakry-\'{E}mery Ricci curvature and the gradient of potential function. As an application, we give a modified proof for a volume comparison and monotonicity of K\"{a}hler-Ricci flow established in a recent work of Tian-Zhang-Zhang-Zhu-Zhu with improved estimate for error term.

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Jintao Ye, Xiaohua Zhu. 2026-04-19. Weighted volume comparison and monotonicity for $L^p$-bound of Bakry-\'{E}mery Ricci curvature. https://arxiv.org/abs/2604.17367

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