Estimate of isodiametric constant for closed surfaces

2014/07/31 by Takashi Shioya, Shioya, Takashi
Mathematics · #53C20 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1407.8275

openalex publication_date 2014/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an explicit estimate of the area of a closed surface by the diameter and a lower bound of curvature. This is better than Calabi-Cao's estimate for a nonnegatively curved two-sphere.

Related

• On the geodesic diameter of surfaces with involutive isometry
• Surfaces of small diameter with large width
• Double Bubbles Minimize
• The Sphere Covering Inequality and Its Applications
• Quantitative stability in the isodiametric inequality via the\n isoperimetric inequality