Zobrazeno 1 - 10
of 4 871
pro vyhledávání: '"rectifiability"'
Autor:
Pertti Mattila
Rectifiable sets, measures, currents and varifolds are foundational concepts in geometric measure theory. The last four decades have seen the emergence of a wealth of connections between rectifiability and other areas of analysis and geometry, includ
In this work, we deal with Delone sets and their rectifiability under different classes of regularity. By pursuing techniques developed by Rivi\`ere and Ye, and Aliste-Prieto, Coronel and Gambaudo, we give sufficient conditions for a Delone set to be
Externí odkaz:
http://arxiv.org/abs/2410.14933
Autor:
Hoffman, John
We provide new characterizations of the $BMO$-Sobolev space $I_{\alpha}(BMO)$ for the range $0 < \alpha <2$. When $0 < \alpha <1$, our characterizations are in terms of square functions measuring multiscale approximation of constants, and when $1 \le
Externí odkaz:
http://arxiv.org/abs/2410.11724
We prove that the singular set of an $m$-dimensional integral current $T$ in $\mathbb{R}^{n + m}$, semicalibrated by a $C^{2, \kappa_0}$ $m$-form $\omega$ is countably $(m - 2)$-rectifiable. Furthermore, we show that there is a unique tangent cone at
Externí odkaz:
http://arxiv.org/abs/2409.03037
Autor:
Dąbrowski, Damian
The Favard length of a Borel set $E\subset\mathbb{R}^2$ is the average length of its orthogonal projections. We prove that if $E$ is Ahlfors 1-regular and it has large Favard length, then it contains a big piece of a Lipschitz graph. This gives a qua
Externí odkaz:
http://arxiv.org/abs/2408.03919
Autor:
Caamaño, Iván, Durand-Cartagena, Estíbalitz, Jaramillo, Jesús Á., Prieto, Ángeles, Soultanis, Elefterios
We combine Kirchheim's metric differentials with Cheeger charts in order to establish a non-embeddability principle for any collection $\mathcal C$ of Banach (or metric) spaces: if a metric measure space $X$ bi-Lipschitz embeds in some element in $\m
Externí odkaz:
http://arxiv.org/abs/2403.18440
Autor:
Donne, Enrico Le, Nalon, Luca
We consider 2-step free-Carnot groups equipped with sub-Finsler distances. We prove that the metric spheres are codimension-one rectifiable from the Euclidean viewpoint. The result is obtained by studying how the Lipschitz constant for the distance f
Externí odkaz:
http://arxiv.org/abs/2403.10196
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