Zobrazeno 1 - 10
of 100
pro vyhledávání: '"Badger Matthew"'
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, Vellis Vyron
Publikováno v:
Analysis and Geometry in Metric Spaces, Vol 9, Iss 1, Pp 90-119 (2021)
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 attractor of an IFS is locally connected and path-connected. We give a qua
Externí odkaz:
https://doaj.org/article/0c87905a11d6469086eb3426c0600bc0
Autor:
Badger Matthew, Schul Raanan
Publikováno v:
Analysis and Geometry in Metric Spaces, Vol 5, Iss 1, Pp 1-39 (2017)
A measure is 1-rectifiable if there is a countable union of finite length curves whose complement has zero measure. We characterize 1-rectifiable Radon measures μ in n-dimensional Euclidean space for all n ≥ 2 in terms of positivity of the lower d
Externí odkaz:
https://doaj.org/article/b8b65633af424a67aff0410686fe5c7b
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