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Wild examples of countably rectifiable sets

Autor: Sean McCurdy, Max Goering

Publikováno v: Annales Fennici Mathematici

We study the geometry of sets based on the behavior of the Jones function, $J_{E}(x) = \int_{0}^{1} \beta_{E;2}^{1}(x,r)^{2} \frac{dr}{r}$. We construct two examples of countably 1-rectifiable sets in $\mathbf{R}^{2}$ with positive and finite \(\

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5a08ee0cacb7d7ea48c6c7f97b0afca8
https://doi.org/10.5186/aasfm.2021.4632

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Menger curvatures and $$\varvec{C^{1,\alpha }}$$ rectifiability of measures

Autor: Max Goering, Silvia Ghinassi

Publikováno v: Archiv der Mathematik. 114:419-429

We further develop the relationship between $$\beta $$-numbers and discrete curvatures to provide a new proof that under weak density assumptions, finiteness of the pointwise discrete curvature $${\text {curv}}^{\alpha }_{\mu ;2}(x,r)$$ at $$\mu $$-a

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::4d515f28e4096eb6f2074cb12283e11c
https://doi.org/10.1007/s00013-019-01414-6

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Families of well approximable measures

Autor: Max Goering, Christian Weiß, Samantha Fairchild

We provide an algorithm to approximate a finitely supported discrete measure μ by a measure νN corresponding to a set of N points so that the total variation between μ and νN has an upper bound. As a consequence if μ is a (finite or infinitely s

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http://arxiv.org/abs/2003.13122

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Two Phase Free Boundary Problem for Poisson Kernels

Autor: Simon Bortz, Max Engelstein, Max Goering, Tatiana Toro, Zihui Zhao

We provide a potential theoretic characterization of vanishing chord-arc domains under minimal assumptions. In particular we show that, if a domain has Ahlfors regular boundary, the oscillation of the logarithm of the interior and exterior Poisson ke

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6492d9059feeaccc83ebf69c72248333
http://arxiv.org/abs/1908.03033

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Numerical Investigation of Metrics for Epidemic Processes on Graphs

Autor: Caterina Scoglio, Pietro Poggi-Corradini, Max Goering, Faryad Darabi Sahneh, Nathan Albin

Publikováno v: ACSSC

This study develops the epidemic hitting time (EHT) metric on graphs measuring the expected time an epidemic starting at node $a$ in a fully susceptible network takes to propagate and reach node $b$. An associated EHT centrality measure is then compa

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c82f261b79d69bf2a7d86e2bd49f7bc1
http://arxiv.org/abs/1511.07893

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