Poincaré inequalities and uniform rectifiability

Autor: Jonas Azzam

Publikováno v: Revista Matemática Iberoamericana. 37:2161-2190

We show that any d-Ahlfors regular subset of Rn supporting a weak (1,d)-Poincare inequality with respect to surface measure is uniformly rectifiable.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::8329205dc066c819d95cec2cb6589a48
https://doi.org/10.4171/rmi/1258

The weak lower density condition and uniform rectifiability

Autor: Jonas Azzam, Matthew Hyde

Publikováno v: Annales Fennici Mathematici

We show that an Ahlfors $d$-regular set $E$ in $\mathbb{R}^{n}$ is uniformly rectifiable if the set of pairs $(x,r)\in E\times (0,\infty)$ for which there exists $y \in B(x,r)$ and $00$. To prove this, we generalize a result of Schul by proving, if $

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::02bc8ff9da68a66e678a8039e96d714f
http://wrap.warwick.ac.uk/166756/1/WRAP-weak-lower-density-condition-uniform-rectifiability-Hyde-2022.pdf

Tangents, rectifiability, and corkscrew domains

Autor: Jonas Azzam

Publikováno v: Recercat: Dipósit de la Recerca de Catalunya
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Azzam, J 2018, ' Tangents, rectifiability, and corkscrew domains ', Publicacions Matemàtiques, vol. 62, no. 1, pp. 161-167 . < https://arxiv.org/abs/1505.03960 >
Recercat. Dipósit de la Recerca de Catalunya
instname
Publicacions Matemàtiques; Vol. 62, Núm. 1 (2018); p. 161-176
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona
Publ. Mat. 62, no. 1 (2018), 161-176

In a recent paper, Cs\"ornyei and Wilson prove that curves in Euclidean space of $\sigma$-finite length have tangents on a set of positive $\mathscr{H}^{1}$-measure. They also show that a higher dimensional analogue of this result is not possible wit

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0cd8cd064fe5c726c37d50090584af75
http://hdl.handle.net/2072/417219

Some remarks on the Lipschitz regularity of Radon transforms

Autor: Jonathan Hickman, Sean Li, Jonas Azzam

Publikováno v: Azzam, J, Li, S & Hickman, J 2018, ' Some remarks on the Lipschitz regularity of Radon transforms ', Proceedings of the american mathematical society, vol. 146, no. 10, pp. 4331-4337 . https://doi.org/10.1090/proc/14083

A set in the Euclidean plane is constructed whose image under the classical Radon transform is Lipschitz in every direction. It is also shown that, under mild hypotheses, for any such set the function which maps a direction to the corresponding Lipsc

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b64dabcdcf959d511eaf258253fc31d0
https://doi.org/10.1090/proc/14083

On a two-phase problem for harmonic measure in general domains

Autor: Mihalis Mourgoglou, Alexander Volberg, Xavier Tolsa, Jonas Azzam

Publikováno v: Azzam, J, Mourgoglou, M, Tolsa, X & Volberg, A 2019, ' On a two-phase problem for harmonic measure in general domains ', American Journal of Mathematics, vol. 141, no. 5, pp. 1259-1279 . https://doi.org/10.1353/ajm.2019.0032

We show that, for disjoint domains in the Euclidean space, mutual absolute continuity of their harmonic measures implies absolute continuity with respect to surface measure and rectifiability in the intersection of their boundaries. This improves on

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::452fcea25d5fe49c11884b3a65e8650e
https://hdl.handle.net/20.500.11820/57d747cb-a61f-4ff9-a173-05130200e34b