Isoperimetric inequalities on minimal submanifolds of space forms

Jaigyoung Choe, Robert D Gulliver

Research output: Contribution to journalArticlepeer-review

35 Scopus citations

Abstract

For a domain U on a certain k-dimensional minimal submanifold of S n or H n, we introduce a "modified volume"M(U) of U and obtain an optimal isoperimetric inequality for U k k ω k M (D) k-1 ≤Vol(∂D) k, where ω k is the volume of the unit ball of R k . Also, we prove that if D is any domain on a minimal surface in S + n (or H n, respectively), then D satisfies an isoperimetric inequality 2π A≤L 2+A2 (2π A≤L2-A2 respectively). Moreover, we show that if U is a k-dimensional minimal submanifold of H n, then (k-1) Vol(U)≤Vol(∂U).

Original languageEnglish (US)
Pages (from-to)169-189
Number of pages21
JournalManuscripta Mathematica
Volume77
Issue number1
DOIs
StatePublished - Dec 1 1992

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