Isoperimetric regions in cones
نویسندگان
چکیده
منابع مشابه
Isoperimetric Regions in Cones
We consider cones C = 0 × Mn and prove that if the Ricci curvature of C is nonnegative, then geodesic balls about the vertex minimize perimeter for given volume. If strict inequality holds, then they are the only stable regions.
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We examine the least-perimeter way to enclose given area or volume in various spaces including some spaces with density.
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This is a very nice paper, looking at isoperimetric problems in various surfaces, though the paper’s title indicates it considers isoperimetric problems in general spaces. It would be a much better and unified paper, in particular more accessible to undergraduates, if the abstract and title reflected that the results center on abstract surfaces rather than abstract spaces. I would recommend tha...
متن کاملCharacterization of Isoperimetric Sets inside Almost-convex Cones
In this note we characterize isoperimetric regions inside almostconvex cones. More precisely, as in the case of convex cones, we show that isoperimetric sets are given by intersecting the cone with a ball centered at the origin.
متن کاملIsoperimetric regions in surfaces and in surfaces with density
We study the isoperimetric problem, the least-perimeter way to enclose given area, in various surfaces. For example, in two-dimensional Twisted Chimney space, a twodimensional analog of one of the ten flat, orientable models for the universe, we prove that isoperimetric regions are round discs or strips. In the Gauss plane, defined as the Euclidean plane with Gaussian density, we prove that in ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2002
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-02-02983-5