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arXiv · 1610.07043

The Log Convex Density Conjecture in Hyperbolic Space

Leonardo Di Giosia·Jahangir Habib·Lea Kenigsberg·Dylanger Pittman·Weitao Zhu
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Abstract

The isoperimetric problem with a density or weighting seeks to enclose prescribed weighted area with minimum weighted perimeter. According to Chambers' recent proof of the Log Convex Density Conjecture, for many densities on $\mathbb{R}^n$ the answer is a sphere about the origin. We generalize his results from $\mathbb{R}^n$ to $\mathbb{H}^n$ with related but different volume and perimeter densities.

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Leonardo Di Giosia, Jahangir Habib, Lea Kenigsberg, Dylanger Pittman, Weitao Zhu. 2016-10-22. The Log Convex Density Conjecture in Hyperbolic Space. https://arxiv.org/abs/1610.07043

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