Zobrazeno 1 - 10
of 101
pro vyhledávání: '"Badger, Matthew"'
Autor:
Badger, Matthew, Schul, Raanan
We prove that for all integers $2\leq m\leq d-1$, there exists doubling measures on $\mathbb{R}^d$ with full support that are $m$-rectifiable and purely $(m-1)$-unrectifiable in the sense of Federer (i.e. without assuming $\mu\ll\mathcal{H}^m$). The
Externí odkaz:
http://arxiv.org/abs/2309.01283
In Kenig and Toro's two-phase free boundary problem, one studies how the regularity of the Radon-Nikodym derivative $h= d\omega^-/d\omega^+$ of harmonic measures on complementary NTA domains controls the geometry of their common boundary. It is now k
Externí odkaz:
http://arxiv.org/abs/2210.17531
Autor:
Badger, Matthew, McCurdy, Sean
We prove that in any Banach space the set of windows in which a rectifiable curve resembles two or more straight line segments is quantitatively small with constants that are independent of the curve, the dimension of the space, and the choice of nor
Externí odkaz:
http://arxiv.org/abs/2208.10288
Autor:
Badger, Matthew, Genschaw, Alyssa
For every $n\geq 2$, Bourgain's constant $b_n$ is the largest number such that the (upper) Hausdorff dimension of harmonic measure is at most $n-b_n$ for every domain in $\mathbb{R}^n$ on which harmonic measure is defined. Jones and Wolff (1988) prov
Externí odkaz:
http://arxiv.org/abs/2205.15101
We continue to develop a program in geometric measure theory that seeks to identify how measures in a space interact with canonical families of sets in the space. In particular, extending a theorem of the first author and R. Schul in Euclidean space,
Externí odkaz:
http://arxiv.org/abs/2109.06753
Autor:
Badger, Matthew, Genschaw, Alyssa
We examine caloric measures $\omega$ on general domains in $\mathbb{R}^{n+1} = \mathbb{R}^n\times\mathbb{R}$ (space $\times$ time) from the perspective of geometric measure theory. On one hand, we give a direct proof of a consequence of a theorem of
Externí odkaz:
http://arxiv.org/abs/2108.12340
In this article, we prove that for a broad class of second order elliptic PDEs, including the Laplacian, the zero sets of solutions to the Dirichlet problem are smooth for "generic" $L^2$ data. When the zero set of a solution (e.g. a harmonic functio
Externí odkaz:
http://arxiv.org/abs/2108.08261
Publikováno v:
Analysis and Geometry in Metric Spaces, Vol 11, Iss 1, Pp 35-55 (2023)
We continue to develop a program in geometric measure theory that seeks to identify how measures in a space interact with canonical families of sets in the space. In particular, extending a theorem of M. Badger and R. Schul in Euclidean space, for an
Externí odkaz:
https://doaj.org/article/cbf50c31be274108ac551616e6474aab
Autor:
Badger, Matthew, Naples, Lisa
For all $1\leq m\leq n-1$, we investigate the interaction of locally finite measures in $\mathbb{R}^n$ with the family of $m$-dimensional Lipschitz graphs. For instance, we characterize Radon measures $\mu$, which are carried by Lipschitz graphs in t
Externí odkaz:
http://arxiv.org/abs/2007.08503
Autor:
Badger, Matthew, McCurdy, Sean
The Analyst's Traveling Salesman Problem is to find a characterization of subsets of rectifiable curves in a metric space. This problem was introduced and solved in the plane by Jones in 1990 and subsequently solved in higher-dimensional Euclidean sp
Externí odkaz:
http://arxiv.org/abs/2002.11878