Quantitative Fatou Theorems and Uniform Rectifiability
Simon Bortz, Steve Hofmann
TL;DR
This paper demonstrates that a specific quantitative Fatou Theorem can be used to characterize uniform rectifiability in codimension 1, linking boundary behavior to geometric regularity.
Contribution
It establishes a new characterization of uniform rectifiability through a quantitative Fatou Theorem in the codimension 1 setting.
Findings
Quantitative Fatou Theorem characterizes uniform rectifiability
New link between boundary behavior and geometric regularity
Advances understanding of rectifiability in geometric measure theory
Abstract
We show that a suitable quantitative Fatou Theorem characterizes uniform rectifiability in the codimension 1 case.
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