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arXiv · 2509.23182

Spectral comparison and splitting theorems for the infinity-Bakry-Emery Ricci curvature

Jia-Yong Wu
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Abstract

In this paper, we prove the diameter comparison, the global weighted volume comparison and the splitting theorem in weighted manifolds when the infinity-Bakry-Emery Ricci curvature has a lower bound in the spectrum sense. Our results extend Antonelli-Xu's spectral Bonnet-Myers and Bishop-Gromov theorems, and Antonelli-Pozzetta-Xu's spectral splitting theorem to weighted manifolds. Our results are also some supplements of Chu-Hao's spectral diameter and global volume comparisons, and Yeung's spectral splitting theorem in weighted manifolds.

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Jia-Yong Wu. 2025-09-27. Spectral comparison and splitting theorems for the infinity-Bakry-Emery Ricci curvature. https://doi.org/10.1007/s11118-026-10292-x

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