manuscripta mathematica

, Volume 77, Issue 1, pp 169–189

Isoperimetric inequalities on minimal submanifolds of space forms


  • Jaigyoung Choe
    • Department of MathematicsPostech
  • Robert Gulliver
    • School of MathematicsUniversity of Minnesota

DOI: 10.1007/BF02567052

Cite this article as:
Choe, J. & Gulliver, R. Manuscripta Math (1992) 77: 169. doi:10.1007/BF02567052


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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© Springer-Verlag 1992