Estimate of isodiametric constant for closed surfaces
Takashi Shioya
TL;DR
This paper provides an explicit estimate of the area of closed surfaces based on diameter and curvature bounds, improving previous estimates for nonnegatively curved two-spheres.
Contribution
It introduces a new, sharper estimate for the area of closed surfaces using diameter and curvature, surpassing prior results for specific cases.
Findings
Explicit area estimate based on diameter and curvature
Improved bounds for nonnegatively curved two-spheres
Enhanced understanding of geometric inequalities on surfaces
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.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Point processes and geometric inequalities