The isoperimetric problem on surfaces of revolution of decreasing Gauss curvature

Authors
Morgan, F Hutchings, M Howards, H
Citation
F. Morgan et al., The isoperimetric problem on surfaces of revolution of decreasing Gauss curvature, T AM MATH S, 352(11), 2000, pp. 4889-4909
Citations number
28
Categorie Soggetti
Mathematics
Journal title
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029947 → ACNP
Volume
352
Issue
11
Year of publication
2000
Pages
4889 - 4909
Database
ISI
SICI code
0002-9947(2000)352:11<4889:TIPOSO>2.0.ZU;2-9
Abstract
We prove that the least-perimeter way to enclose prescribed area in the pla ne with smooth, rotationally symmetric, complete metric of nonincreasing Ga uss curvature consists of one or two circles, bounding a disc, the compleme nt of a disc, or an annulus. We also provide a new isoperimetric inequality in general surfaces with boundary.