Results 11 to 20 of about 85 (68)
On the systole growth in congruence quaternionic hyperbolic manifolds
Bulletin of the London Mathematical Society, Volume 54, Issue 4, Page 1265-1281, August 2022., 2022 Abstract We provide an explicit lower bound for the systole in principal congruence covers of compact quaternionic hyperbolic manifolds. We also prove the optimality of this lower bound.
Vincent Emery +2 more
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Strengthened inequalities for the mean width and the ℓ‐norm
Journal of the London Mathematical Society, Volume 104, Issue 1, Page 233-268, July 2021., 2021 Abstract Barthe proved that the regular simplex maximizes the mean width of convex bodies whose John ellipsoid (maximal volume ellipsoid contained in the body) is the Euclidean unit ball; or equivalently, the regular simplex maximizes the ℓ‐norm of convex bodies whose Löwner ellipsoid (minimal volume ellipsoid containing the body) is the Euclidean unit
Károly J. Böröczky +2 more
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Tangent points of lower content d‐regular sets and β numbers
Journal of the London Mathematical Society, Volume 101, Issue 2, Page 530-555, April 2020., 2020 Abstract Given a lower content d‐regular set in Rn, we prove that the subset of points in E where a certain Dini‐type condition on the so‐called Jones β numbers holds coincides with the set of tangent points of E, up to a set of Hd‐measure zero. The main point of our result is that Hd|E is not σ‐finite; because of this, we use a certain variant of the ...
Michele Villa
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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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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
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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 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
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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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