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arXiv:1604.02768 [math.DG]AbstractReferencesReviewsResources

Isoperimetric Regions in Nonpositively Curved Manifolds

Joel Hass

Published 2016-04-11Version 1

Isoperimetric regions minimize the size of their boundaries among all regions with the same volume. In Euclidean and Hyperbolic space, isoperimetric regions are round balls. We show that isoperimetric regions in two and three-dimensional nonpositively curved manifolds are not necessarily balls, and need not even be connected.

Categories: math.DG
Subjects: 53A10, 52A38
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