5 papers
Radon measures and Lipschitz graphs
Matthew Badger, Lisa Naples
For all , we investigate the interaction of locally finite measures in with the family of -dimensional Lipschitz graphs. For instance, we charact…
Hölder parameterization of iterated function systems and a self-affine phenomenon
Matthew Badger, Vyron Vellis
We investigate the Hölder geometry of curves generated by iterated function systems (IFS) in a complete metric space. A theorem of Hata from 1985 asserts that every connected attra…
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…
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…
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…