2017•Rose-Hulman Scholar (Rose–Hulman Institute of Technology)Requires access
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 Euclidean log convex density theorem, proved by Gregory Chambers in 2015, asserts that in Euclidean space with a log convex density spheres about the origin are isoperimetric. We provide a partial extension to hyperbolic space in which volume and perimeter densities are related but different.