21 citations · 37 across the 15 of their papers we have counts for
6 papers · 1 filter
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…
Soap Film Solutions to Plateau's Problem
Jenny Harrison
Plateau's problem is to show the existence of an area minimizing surface with a given boundary, a problem posed by Lagrange in 1760. Experiments conducted by Plateau showed that an…
On Plateau's Problem for Soap Films with a Bound on Energy
Jenny Harrison
We prove existence and a.e. regularity of an area minimizing soap film with a bound on energy spanning a given Jordan curve in R^3. The energy of a film is defined to be the sum of…
Stokes' theorem for nonsmooth chains
Jenny Harrison
Much of the vast literature on the integral during the last two centuries concerns extending the class of integrable functions. In contrast, our viewpoint is akin to that taken by…