5 citations · 11 across the 7 of their papers we have counts for
4 papers · 1 filter
Optimal monohedral tilings of hyperbolic surfaces
Leonardo Di Giosia, Jahangir Habib, Jack Hirsch +6
The hexagon is the least-perimeter tile in the Euclidean plane for any given area. On hyperbolic surfaces, this "isoperimetric" problem differs for every given area, as solutions d…
Double Bubbles on the Real Line with Log-Convex Density
Eliot Bongiovanni, Leonardo Di Giosia, Alejandro Diaz +6
The classic double bubble theorem says that the least-perimeter way to enclose and separate two prescribed volumes in is the standard double bubble. We seek the opti…
The Log Convex Density Conjecture in Hyperbolic Space
Leonardo Di Giosia, Jahangir Habib, Lea Kenigsberg +2
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 Conv…
Balls Isoperimetric in with Volume and Perimeter Densities and
Leonardo Di Giosia, Jahangir Habib, Lea Kenigsberg +2
We have discovered a "little" gap in our proof of the sharp conjecture that in with volume and perimeter densities and , balls about the origin are unique…