Isoperimetric inequalities on minimal submanifolds of space forms |
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Authors: | Jaigyoung Choe Robert Gulliver |
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Affiliation: | (1) Department of Mathematics, Postech, P.O. Box 125, Pohang, South Korea;(2) School of Mathematics, University of Minnesota, 55455 Minneapolis, Minnesota, USA |
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Abstract: | For a domainU on a certaink-dimensional minimal submanifold ofS n orH n, we introduce a “modified volume”M(U) ofU and obtain an optimal isoperimetric inequality forU k k ω k M (D) k-1 ≤Vol(∂D) k , where ω k is the volume of the unit ball ofR k . Also, we prove that ifD is any domain on a minimal surface inS + n (orH n, respectively), thenD satisfies an isoperimetric inequality2π A≤L 2+A2 (2π A≤L2−A2 respectively). Moreover, we show that ifU is ak-dimensional minimal submanifold ofH n, then(k−1) Vol(U)≤Vol(∂U). Supported in part by KME and GARC |
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