5 citations · 9 across the 9 of their papers we have counts for
4 papers · 1 filter
Reifenberg's Isoperimetric Inequality Revisited
Harrison Pugh
We prove a generalization of Reifenberg's isoperimetric inequality. The main result of this paper is used to establish existence of a minimizer for an anisotropically-weighted area…
General Methods of Elliptic Minimization
Jenny Harrison, Harrison Pugh
We provide new general methods in the calculus of variations for the anisotropic Plateau problem in arbitrary dimension and codimension. A new direct proof of Almgren's 1968 existe…
Plateau's Problem: What's Next
Jenny Harrison, Harrison Pugh
Plateau's problem is not a single conjecture or theorem, but rather an abstract framework, encompassing a number of different problems in several related areas of mathematics. In i…
Solutions to the Reifenberg Plateau problem with cohomological spanning conditions
J. Harrison, H. Pugh
We prove existence and regularity of minimizers for Hölder densities over general surfaces of arbitrary dimension and codimension in \(\R^n \), satisfying a cohomological boundary…