2015/04/21 by Homare Tadano, Tadano, Homare · 1 citation
Mathematics · Physics and Astronomy · #53C25 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Primary 53C21 #Secondary 53C20
paper · pdf · doi:10.48550/arxiv.1504.05384
openalex publication_date 2015/04/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper, we shall give a new upper diameter estimate for complete Riemannian manifolds in the case that the Bakry-Émery Ricci curvature has a positive lower bound and the norm of the potential function has an upper bound. Our diameter estimate improves previous ones obtained by Wei and Wylie (J. Differential Geom. 83, 377--405, 2009) and Limoncu (Math. Z. 271, 715--722, 2012). As an application, we shall give an upper diameter bound for compact Ricci solitons in terms of the maximum value of the scalar curvature. By using such a diameter bound, we shall provide some new sufficient conditions for four-dimensional compact Ricci solitons to satisfy the Hitchin-Thorpe inequality.