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Geometriae Dedicata

, Volume 174, Issue 1, pp 279–285 | Cite as

Estimate of isodiametric constant for closed surfaces

  • Takashi ShioyaEmail author
Original Paper
  • 154 Downloads

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 (J Differ Geom 36(3): 517–549, 1992) estimate for a nonnegatively curved two-sphere.

Keywords

A. D. Alexandrov’s conjecture Isodiametric inequality  Area Diameter Curvature 

Mathematics Subject Classification (2010)

Primary 53C20 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Mathematical InstituteTohoku UniversitySendaiJapan

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