21 citations · 37 across the 15 of their papers we have counts for
18 papers
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…
Spanning via Cech Cohomology
Jenny Harrison, Harrison Pugh
Plateau's problem is to find a surface with minimal area spanning a given boundary. In 1960, Reifenberg and Adams developed a definition for "span" using Čech homology, and variant…
Existence and Soap Film Regularity of Solutions to Plateau's Problem
Jenny Harrison, Harrison Pugh
Plateau's soap film problem is to find a surface of least area spanning a given boundary. We begin with a compact orientable -dimensional submanifold of . If i…
Operator Calculus of Differential Chains and Differential Forms
Jenny Harrison
Differential chains are a proper subspace of de Rham currents given as an inductive limit of Banach spaces endowed with a geometrically defined strong topology. Boundary is a conti…