Výsledky vyhledávání - "Naples, Lisa"

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Asymptotics of maximum distance minimizers

Autor: Alvarado, Enrique G, Catalano, Louisa, Merchán, Tomás, Naples, Lisa

We study the limiting behavior of $r$-maximum distance minimizers and the asymptotics of their $1$-dimensional Hausdorff measures as $r$ tends to zero in several contexts, including situations involving objects of fractal nature.
Comment: 24 pag

Externí odkaz: http://arxiv.org/abs/2309.08055

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Non-existence of cusps for degenerate Alt-Caffarelli functionals

Autor: McCurdy, Sean, Naples, Lisa

We eliminate the existence of cusps in a class of \textit{degenerate} free-boundary problems for the Alt-Caffarelli functional $J_{Q}(v, \Omega):= \int_{\Omega}|\nabla v|^2 + Q^2(x)\chi_{\{v>0\}}dx,$ so-called because $Q(x) = \text{dist}(x, \Gamma)^{

Externí odkaz: http://arxiv.org/abs/2202.00616

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Nilpotent groups and biLipschitz embeddings into $L^1$

Autor: Eriksson-Bique, Sylvester, Gartland, Chris, Donne, Enrico Le, Naples, Lisa, Nicolussi-Golo, Sebastiano

We prove that if a simply connected nilpotent Lie group quasi-isometrically embeds into an $L^1$ space, then it is abelian. We reach this conclusion by proving that every Carnot group that biLipschitz embeds into $L^1$ is abelian. Our proof follows t

Externí odkaz: http://arxiv.org/abs/2112.11402

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Radon measures and Lipschitz graphs

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

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Rectifiability of pointwise doubling measures in Hilbert Space

Autor: Naples, Lisa

In geometric measure theory, there is interest in studying the interaction of measures with rectifiable sets. Here, we extend a theorem of Badger and Schul in Euclidean space to characterize rectifiable pointwise doubling measures in Hilbert space. G

Externí odkaz: http://arxiv.org/abs/2002.07570

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H\'older curves and parameterizations in the Analyst's Traveling Salesman theorem

Autor: Badger, Matthew, Naples, Lisa, Vellis, Vyron

Publikováno v: Adv. Math. 349 (2019), 564-647

We investigate the geometry of sets in Euclidean and infinite-dimensional Hilbert spaces. We establish sufficient conditions that ensure a set of points is contained in the image of a $(1/s)$-H\"older continuous map $f:[0,1]\rightarrow l^2$, with $s>

Externí odkaz: http://arxiv.org/abs/1806.01197

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