Scholarlink

<p>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.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Spectral Comparison and Splitting Theorems for the Infinity-Bakry-Emery Ricci Curvature

  • 期刊论文

  • 发表日期：

    2026年3月13日

查看全文
  • Jia-Yong Wu

摘要

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.