5 citations · 11 across the 7 of their papers we have counts for
7 papers
Convex Solutions to the Virtual Source Reflector Problem
Dylanger Pittman
We greatly expand upon the results of Kochengin, Oliker and Tempeski [S. Kochengin, V. Oliker, O. von Tempeski, On the design of reflectors with prescribed distribution of virtual…
Weak solutions to the near-field reflector problem with spatial restrictions approached with generalized reflectors constructed from ellipsoids
Dylanger Pittman
We motivate then formulate a novel variant of the near-field reflector problem and call it the near-field reflector problem with spatial restrictions. Let be an anisotropic poi…
A constructive proof of the Bollobás-Varopoulos theorem
Dylanger Pittman
The Bollobás-Varopoulos theorem is an analogue of Hall's matching theorem on non-atomic measure spaces. Here we prove a finite version with a completely constructive proof.
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…