The Log Convex Density Conjecture in Hyperbolic Space

Authors

Leonardo Di Giosia, Lewis and Clark College
Jahangir Habib, Williams College
Lea Kenigsberg, Stony Brook University
Dylanger Pittman, Williams College
Weitao Zhu, Williams College

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.

Author Bio

Leo Digiosia graduated Summa Cum Laude from Lewis & Clark College in Portland, OR. He is a member of Phi Beta Kappa and Pi Mu Epsilon as well as a Robert B. Pamplin Fellow. He joined Williams' SMALL REU program with advisor Frank Morgan and the Geometry 2016 research team then presented these results at MathFest 2016 and the Joint Mathematics Meetings in 2017. He will enter a pure math PhD program at Rice University in Fall 2017. When not bounding integrands, Leo can be found cooking and frying chicken for friends and family.

Faculty Sponsor

Frank Morgan

Recommended Citation

Di Giosia, Leonardo; Habib, Jahangir; Kenigsberg, Lea; Pittman, Dylanger; and Zhu, Weitao (2017) "The Log Convex Density Conjecture in Hyperbolic Space," Rose-Hulman Undergraduate Mathematics Journal: Vol. 18: Iss. 1, Article 9.
Available at: https://scholar.rose-hulman.edu/rhumj/vol18/iss1/9