5 citations · 9 across the 9 of their papers we have counts for
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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…
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…