Results 1 to 10 of about 85 (68)
Almost uniform domains and Poincaré inequalities
Transactions of the London Mathematical Society, 2021 Here we show existence of many subsets of Euclidean spaces that, despite having empty interior, still support Poincaré inequalities with respect to the restricted Lebesgue measure.
Sylvester Eriksson‐Bique, Jasun Gong
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A Systematic Study of Multifractal Measures and Dimensions for Image Measures on Moran Sets
Abstract and Applied AnalysisMSC2020 Classification: 28A20, 28A75, 28A78, 28A80 ...
Lixin Guo, Haythem Zyoudi
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Tangent measures of typical measures
, 2015 We prove that for a typical Radon measure μ in ℝd, every non-zero Radon measure is a tangent measure of μ at μ almost every point. This was already shown by T. O'Neil in his Ph.D. thesis from 1994, but we provide a different self-contained proof for this
Sahlsten, Tuomas
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Dilation Type Inequalities for Strongly-Convex Sets in Weighted Riemannian Manifolds
Analysis and Geometry in Metric Spaces, 2021 In this paper, we consider a dilation type inequality on a weighted Riemannian manifold, which is classically known as Borell’s lemma in high-dimensional convex geometry.
Tsuji Hiroshi
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On sets with unit Hausdorff density in homogeneous groups
Forum of Mathematics, Sigma, 2023 It is a longstanding conjecture that given a subset E of a metric space, if E has unit $\mathscr {H}^{\alpha }\llcorner E$ -density almost everywhere, then E is an $\alpha $ -rectifiable set. We prove this conjecture under the assumption that
Antoine Julia, Andrea Merlo
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A Generalization of Archimedes’ Theorem on the Area of a Parabolic Segment
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 Archimedes’ well known theorem on the area of a parabolic segment says that this area is 4/3 of the area of a certain inscribed triangle. In this paper we generalize this theorem to the n-dimensional euclidean space, n ≥ 3.
Grigoryan Armen +2 more
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Analysis and Geometry in Metric Spaces, 2020 This paper studies the Hausdorff dimension of the intersection of isotropic projections of subsets of ℝ2n, as well as dimension of intersections of sets with isotropic planes. It is shown that if A and B are Borel subsets of ℝ2n of dimension greater than
Román-García Fernando
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Isoperimetric and Poincaré Inequalities on Non-Self-Similar Sierpiński Sponges: the Borderline Case
Analysis and Geometry in Metric Spaces, 2022 In this paper we construct a large family of examples of subsets of Euclidean space that support a 1-Poincaré inequality yet have empty interior. These examples are formed from an iterative process that involves removing well-behaved domains, or more ...
Eriksson-Bique Sylvester, Gong Jasun
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Global regularity for minimal sets near a union of two planes [PDF]
, 2016 We discuss the global regularity of 2 dimensional minimal sets that are near a union of two planes, and prove that every global minimal set in R4 that looks like a union of two almost orthogonal planes at infinity is a cone.
Xiangyu Liang, Liang, Xiangyu
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MEASURABLE REALIZATIONS OF ABSTRACT SYSTEMS OF CONGRUENCES
Forum of Mathematics, Sigma, 2020 An abstract system of congruences describes a way of partitioning a space into finitely many pieces satisfying certain congruence relations. Examples of abstract systems of congruences include paradoxical decompositions and $n$-divisibility of actions ...
CLINTON T. CONLEY +2 more
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