The Isoperimetric Problem on Surfaces of Revolution of Decreasing Gauss Curvature
نویسنده
چکیده
We prove that the least-perimeter way to enclose prescribed area in the plane with smooth, rotationally symmetric, complete metric of nonincreasing Gauss curvature consists of one or two circles, bounding a disc, the complement of a disc, or an annulus. We also provide a new isoperimetric inequality in general surfaces with boundary.
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