Results 11 to 20 of about 70 (65)
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
core +2 more sources
Analysis and Geometry in Metric Spaces, 2021 We extend the classical Carathéodory extension theorem to quasiconformal Jordan domains (Y, dY). We say that a metric space (Y, dY) is a quasiconformal Jordan domain if the completion ̄Y of (Y, dY) has finite Hausdorff 2-measure, the boundary ∂Y = ̄Y \ Y
Ikonen Toni
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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, null Tuomas Sahlsten
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Hölder Parameterization of Iterated Function Systems and a Self-Affine Phenomenon
Analysis and Geometry in Metric Spaces, 2021 We investigate the Hölder geometry of curves generated by iterated function systems (IFS) in a complete metric space. A theorem of Hata from 1985 asserts that every connected attractor of an IFS is locally connected and path-connected.
Badger Matthew, Vellis Vyron
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Identifying 1-rectifiable measures in Carnot groups
Analysis and Geometry in Metric Spaces, 2023 We continue to develop a program in geometric measure theory that seeks to identify how measures in a space interact with canonical families of sets in the space. In particular, extending a theorem of M. Badger and R.
Badger Matthew, Li Sean, Zimmerman Scott
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Stagnation zones of ideal flows in long and narrow bands
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 62, Page 3339-3356, 2004., 2004 We investigate stagnation zones of flows of ideal incompressible fluid in narrow and long bands. With the bandwidth being much less than its length, these flows are almost stationary over large subdomains, where their potential functions are almost constant. These subdomains are called s‐zones. We estimate the size and the location of these s‐zones.
V. M. Miklyukov +2 more
wiley +1 more source
Volume Bounds for the Quantitative Singular Strata of Non Collapsed RCD Metric Measure Spaces
Analysis and Geometry in Metric Spaces, 2019 The aim of this note is to generalize to the class of non collapsed RCD(K, N) metric measure spaces the volume bound for the effective singular strata obtained by Cheeger and Naber for non collapsed Ricci limits in [13].
Antonelli Gioacchino +2 more
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A dichotomy of sets via typical differentiability
Forum of Mathematics, Sigma, 2020 We obtain a criterion for an analytic subset of a Euclidean space to contain points of differentiability of a typical Lipschitz function: namely, that it cannot be covered by countably many sets, each of which is closed and purely unrectifiable (has a ...
Michael Dymond, Olga Maleva
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A note on equivalent interval covering systems for Hausdorff dimension on ℝ
International Journal of Mathematics and Mathematical Sciences, Volume 11, Issue 4, Page 643-649, 1988., 1988 The Hausdorff dimension of a set in ℝ is usually defined by considering countable coverings of the set by general intervals. In this note we establish sufficient conditions under which coverings whose members are restricted to a particular family g of intervals will produce the same value for dimension.
C. D. Cutler
wiley +1 more source
LOCAL SET APPROXIMATION: MATTILA–VUORINEN TYPE SETS, REIFENBERG TYPE SETS, AND TANGENT SETS
Forum of Mathematics, Sigma, 2015 We investigate the interplay between the local and asymptotic geometry of a set $A\subseteq \mathbb{R}^{n}$ and the geometry of model sets ${\mathcal{S}}\subset {\mathcal{P}}(\mathbb{R}^{n})$, which approximate $A$ locally uniformly on small scales.
MATTHEW BADGER, STEPHEN LEWIS
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