4 citations · 4 across the 8 of their papers we have counts for
6 papers · 1 filter
Big Pieces of Regular Parabolic (bi-)Lipschitz Images is Equivalent to Parabolic Uniform Rectifiability
Simon Bortz, Matthew Hyde, Mason Sharp
We define the notion of regular parabolic (bi-)Lipschitz images as the parabolic (bi-)Lipschitz maps from -dimensional space time which, up to translation, fix the variable…
Weighted Sobolev Inequalities via the Meyers--Ziemer Framework: Measures, Isoperimetric Inequalities, and Endpoint Estimates
Simon Bortz, Kabe Moen, Andrea Olivo +2
We establish a new global endpoint Sobolev inequality for measures that extends the classical theorem of Meyers-Ziemer by placing a maximal function on the right-hand side. This re…
Coronizations and big pieces in metric spaces
Simon Bortz, John Hoffman, Steve Hofmann +2
We prove that coronizations with respect to arbitrary d-regular sets (not necessarily graphs) imply big pieces squared of these (approximating) sets. This is known (and due to Davi…
Two Phase Free Boundary Problem for Poisson Kernels
Simon Bortz, Max Engelstein, Max Goering +2
We provide a potential theoretic characterization of vanishing chord-arc domains under minimal assumptions. In particular we show that, if a domain has Ahlfors regular boundary, th…
Reifenberg Flatness and Oscillation of the Unit Normal Vector
Simon Bortz, Max Engelstein
We show (under mild topological assumptions) that small oscillation of the unit normal vector implies Reifenberg flatness. We then apply this observation to the study of chord-arc…
Harmonic measure and approximation of uniformly rectifiable sets
Simon Bortz, Steve Hofmann
Let , , be a uniformly rectifiable set of dimension . We show that has big pieces of boundaries of a class of domains which satisfy a 2-si…