Isoperimetric inequalities on minimal submanifolds of space forms |
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| Authors: | Jaigyoung Choe Robert Gulliver |
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| Institution: | (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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| Keywords: | |
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