5 citations · 9 across the 9 of their papers we have counts for
12 papers
Higher Covariant Derivative and the Bundle of Dirac Currents
Harrison Pugh
Using the higher covariant derivative on a manifold equipped with a torsion-free connection, we define a natural surjective bundle map from $ (\otimes(TM))\otimes (\wedg…
The Hopf Algebraic Structure of Finitely Supported Currents on a Lie Group
Harrison Pugh
The space of de Rham currents supported in finitely many points in a Lie group has the structure of a filtered differential graded Hopf algebra. The product is given by convolu…
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…
A Localized Besicovitch-Federer Projection Theorem
Harrison Pugh
The classical Besicovitch-Federer projection theorem implies that the d-dimensional Hausdorff measure of a set in Euclidean space with non-negligible d-unrectifiable part will stri…
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…