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Creators/Authors contains: "Eriksson-Bique, Sylvester"

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  1. ; ; (, Nonlinear Analysis)
    We show that there exists a family of mutually singular doubling measures on Laakso space with respect to which real-valued Lipschitz functions are almost everywhere differentiable. This implies that there exists a measure zero universal differentiability set in Laakso space. Additionally, we show that each of the measures constructed supports a Poincare inequality. 
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    Free, publicly-accessible full text available June 1, 2026
  2. ; (, Transactions of the American Mathematical Society, Series B)
    We show that capacity can be computed with locally Lipschitz functions in locally complete and separable metric spaces. Further, we show that if ( X , d , μ<#comment/> ) (X,d,\mu ) is a locally complete and separable metric measure space, then continuous functions are dense in the Newtonian space N 1 , p ( X ) N^{1,p}(X) . Here the measure μ<#comment/> \mu is Borel and is finite and positive on all metric balls. In particular, we don’t assume properness of X X , doubling of μ<#comment/> \mu or any Poincaré inequalities. These resolve, partially or fully, questions posed by a number of authors, including J. Heinonen, A. Björn and J. Björn. In contrast to much of the past work, our results apply tolocally completespaces X X and dispenses with the frequently used regularity assumptions: doubling, properness, Poincaré inequality, Loewner property or quasiconvexity. 
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  3. ; (, Annales de l'Institut Fourier)
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  4. ; ; (, Proceedings of the American Mathematical Society)
    A quasiconformal tree is a doubling metric tree in which the diameter of each arc is bounded above by a fixed multiple of the distance between its endpoints. In this paper we show that every quasiconformal tree bi-Lipschitz embeds in some Euclidean space, with the ambient dimension and the bi-Lipschitz constant depending only on the doubling and bounded turning constants of the tree. This answers Question 1.6 of David and Vellis [Illinois J. Math. 66 (2022), pp. 189–244]. 
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  5. ; ; ; ; (, Journal of Differential Equations)
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  6. ; ; ; (, Transactions of the American Mathematical Society)
    null (Ed.)
    In this paper, we study the asymptotic behavior of BV functions in complete metric measure spaces equipped with a doubling measure supporting a 1-Poincare inequality. We show that at almost every point x outside the Cantor and jump parts of a BV function, the asymptotic limit of the function is a Lipschitz continuous function of least gradient on a tangent space to the metric space based at x. We also show that, at co-dimension 1 Hausdorff measure almost every measure-theoretic boundary point of a set E of finite perimeter, there is an asymptotic limit set (E)∞ corresponding to the asymptotic expansion of E and that every such asymptotic limit (E)∞ is a quasiminimal set of finite perimeter. We also show that the perimeter measure of (E)∞ is Ahlfors co-dimension 1 regular. 
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  7. ; ; ; (, International Mathematics Research Notices)
    null (Ed.)
    Abstract We show that the 1st-order Sobolev spaces $$W^{1,p}(\Omega _\psi ),$$  $$1<p\leq \infty ,$$ on cuspidal symmetric domains $$\Omega _\psi $$ can be characterized via pointwise inequalities. In particular, they coincide with the Hajłasz–Sobolev spaces $$M^{1,p}(\Omega _\psi )$$. 
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  8. ; ; (, Journal of Functional Analysis)
    null (Ed.)
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  9. ; (, Advances in Mathematics)
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  10. ; (, Transactions of the American Mathematical Society)
    null (Ed.)
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