manuscripta mathematica

, Volume 77, Issue 1, pp 169–189

Isoperimetric inequalities on minimal submanifolds of space forms

  • Jaigyoung Choe
  • Robert Gulliver
Article

Abstract

For a domainU on a certaink-dimensional minimal submanifold ofSn orHn, we introduce a “modified volume”M(U) ofU and obtain an optimal isoperimetric inequality forU kk ωkM (D)k-1Vol(∂D)k, where ωk is the volume of the unit ball ofRk. Also, we prove that ifD is any domain on a minimal surface inS+n (orHn, respectively), thenD satisfies an isoperimetric inequality2π A≤L2+A2 (2π A≤L2−A2 respectively). Moreover, we show that ifU is ak-dimensional minimal submanifold ofHn, then(k−1) Vol(U)≤Vol(∂U).

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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Jaigyoung Choe
    • 1
  • Robert Gulliver
    • 2
  1. 1.Department of MathematicsPostechPohangSouth Korea
  2. 2.School of MathematicsUniversity of MinnesotaMinneapolisUSA

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