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arXiv · 1604.02768

Isoperimetric Regions in Nonpositively Curved Manifolds

Joel Hass
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Abstract

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.

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Joel Hass. 2016-04-11. Isoperimetric Regions in Nonpositively Curved Manifolds. https://arxiv.org/abs/1604.02768

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