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math.AP2018
Regularity of the singular set in a two-phase problem for harmonic measure with Hölder data
Matthew Badger, Max Engelstein, Tatiana Toro
In non-variational two-phase free boundary problems for harmonic measure, we examine how the relationship between the interior and exterior harmonic measures of a domain $Ω\subset…
math.CA2018
Hölder curves and parameterizations in the Analyst's Traveling Salesman theorem
Matthew Badger, Lisa Naples, Vyron Vellis
We investigate the geometry of sets in Euclidean and infinite-dimensional Hilbert spaces. We establish sufficient conditions that ensure a set of points is contained in the image o…
math.CA2018
Generalized rectifiability of measures and the identification problem
Matthew Badger
One goal of geometric measure theory is to understand how measures in the plane or higher dimensional Euclidean space interact with families of lower dimensional sets. An important…