Persona:
Durand Cartagena, Estibalitz

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0000-0001-6469-3633
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Durand Cartagena
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Estibalitz
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2018 - 201942020 - 20231
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Mostrando 1 - 5 de 5
  • Miniatura
    Publicación
    Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a 1-Poincaré inequality
    (De Gruyter, 2019-01-30) Durand Cartagena, Estibalitz; Eriksson Bique, Sylvester; Korte, Riikka; Shanmugalingam, Nageswari
    We consider two notions of functions of bounded variation in complete metric measure spaces, one due to Martio and the other due to Miranda Jr. We show that these two notions coincide if the measure is doubling and supports a 1-Poincaré inequality. In doing so, we also prove that if the measure is doubling and supports a 1-Poincaré inequality, then the metric space supports a Semmes family of curves structure.
  • Miniatura
    Publicación
    Self-contracted curves are gradient flows of convex functions
    (American Mathematical Society, 2019-02-14) Durand Cartagena, Estibalitz; Lemenant, Antoine
    In this paper we prove that any C1, 1/2 curve in Rn, is the solution of the gradient flow equation for some C1 convex function f, if and only if it is strongly self-contracted.
  • Miniatura
    Publicación
    Existence and uniqueness of ∞-harmonic functions under assumption of ∞-Poincaré inequality
    (Springer Nature, 2018-08-22) Durand Cartagena, Estibalitz; Jaramillo, Jesús A.; https://orcid.org/0000-0002-0197-6449; https://orcid.org/0000-0002-2891-5064
    Given a complete metric measure space whose measure is doubling and supports an ∞- Poincar´e inequality, and a bounded domain Ω in such a space together with a Lipschitz function f : ∂Ω → R, we show the existence and uniqueness of an ∞-harmonic extension of f to Ω. To do so, we show that there is a metric that is bi-Lipschitz equivalent to the original metric, such that with respect to this new metric the metric space satisfies an ∞- weak Fubini property and that a function which is ∞-harmonic in the original metric must also be ∞-harmonic with respect to the new metric. We also show that if the metric on the metric space satisfies an ∞-weak Fubini property, then the notion of ∞-harmonic functions coincide with the notion of AMLEs proposed by Aronsson. The notion of ∞-harmonicity is in general distinct from the notion of strongly absolutely minimizing Lipschitz extensions found in [13, 25, 26], but coincides when the metric space supports a p-Poincar´e inequality for some finite p ≥ 1.
  • Miniatura
    Publicación
    Doubling constants and spectral theory on graphs
    (Elsevier, 2023-02-08) Durand Cartagena, Estibalitz; Soria, Javier; Tradacete, Pedro
    We study the least doubling constant among all possible doubling measures defined on a (finite or infinite) graph G. We show that this constant can be estimated from below by 1+r(AG), where r(AG) is the spectral radius of the adjacency matrix of G, and study when both quantities coincide. We also illustrate how amenability of the automorphism group of a graph can be related to finding doubling minimizers. Finally, we give a complete characterization of graphs with doubling constant smaller than 3, in the spirit of Smith graphs.
  • Miniatura
    Publicación
    Sierpinski type fractals are differentiably trivial
    (Finnish Mathematical Society, 2019-08-01) Durand Cartagena, Estibalitz; Jasun Gong; Jesús A. Jaramillo; https://orcid.org/0000-0002-0197-6449
    In this note we study generalized differentiability of functions on a class of fractals in Euclidean spaces. Such sets are not necessarily self-similar, but satisfy a weaker “scale-similar” property; in particular, they include the non self similar carpets introduced by Mackay–Tyson– Wildrick [12] but with different scale ratios. Specifically we identify certain geometric criteria for these fractals and, in the case that they have zero Lebesgue measure, we show that such fractals cannot support nonzero derivations in the sense of Weaver [16]. As a result (Theorem 26) such fractals cannot support Alberti representations and in particular, they cannot be Lipschitz differentiability spaces in the sense of Cheeger [3] and Keith [9].