Results 31 to 40 of about 7,382 (157)
Hausdorff vs Gromov-Hausdorff distances
, 2023 Let $M$ be a closed Riemannian manifold and let $X\subseteq M$. If the sample $X$ is sufficiently dense relative to the curvature of $M$, then the Gromov-Hausdorff distance between $X$ and $M$ is bounded from below by half their Hausdorff distance, namely $d_{GH}(X,M) \ge \frac{1}{2} d_H(X,M)$.
Adams, Henry +3 more
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Towards the boundary of the fine curve graph
Journal of Topology, Volume 19, Issue 2, June 2026.Abstract The fine curve graph was introduced as a geometric tool to study homeomorphisms of surfaces. In this paper, we study the Gromov boundary of this space and the local topology near points associated with certain foliations and laminations. We then give several applications including finding dynamically explicit elements with positive stable ...
Jonathan Bowden +2 more
wiley +1 more source
Gromov--Hausdorff Distance to Simplexes
, 2019 Geometric characteristics of metric spaces that appear in formulas of the Gromov--Hausdorff distances from these spaces to so-called simplexes, i.e., to the metric spaces, all whose non-zero distances are the same are studied. The corresponding calculations essentially use geometry of partitions of these spaces. In the finite case, it gives the lengths
Grigor'ev, D. S. +2 more
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Degree theory for 4‐dimensional asymptotically conical gradient expanding solitons
Communications on Pure and Applied Mathematics, Volume 79, Issue 5, Page 1151-1298, May 2026.Abstract We develop a new degree theory for 4‐dimensional, asymptotically conical gradient expanding solitons. Our theory implies the existence of gradient expanding solitons that are asymptotic to any given cone over S3$S^3$ with non‐negative scalar curvature. We also obtain a similar existence result for cones whose link is diffeomorphic to S3/Γ$S^3/\
Richard H. Bamler, Eric Chen
wiley +1 more source
Interleaving and Gromov-Hausdorff distance
, 2017 35 pages, v3: changed title and added references to uses of interleaving (Section 1.3)
Bubenik, Peter +2 more
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Gromov-Hausdorff distance for quantum metric spaces [PDF]
Memoirs of the American Mathematical Society, 2004 By a quantum metric space we mean a C^*-algebra (or more generally an order-unit space) equipped with a generalization of the Lipschitz seminorm on functions which is defined by an ordinary metric. We develop for compact quantum metric spaces a version of Gromov-Hausdorff distance.
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Gromov-Hausdorff Distance and Borsuk Number
, 2022 It is the same publication as arXiv:2203.04030.
Ivanov, Alexander, Tuzhilin, Alexey
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Graphical small cancellation and hyperfiniteness of boundary actions
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract We study actions of (infinitely presented) graphical small cancellation groups on the Gromov boundaries of their coned‐off Cayley graphs. We show that a class of graphical small cancellation groups, including (infinitely presented) classical small cancellation groups, admit hyperfinite boundary actions, more precisely, the orbit equivalence ...
Chris Karpinski +2 more
wiley +1 more source
A Compactness Theorem for The Dual Gromov-Hausdorff Propinquity [PDF]
, 2015 We prove a compactness theorem for the dual Gromov-Hausdorff propinquity as a noncommutative analogue of the Gromov compactness theorem for the Gromov-Hausdorff distance.
Latremoliere, Frederic
core +2 more sources
Circle packings, renormalizations, and subdivision rules
Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.Abstract In this paper, we use iterations of skinning maps on Teichmüller spaces to study circle packings and develop a renormalization theory for circle packings whose nerves satisfy certain subdivision rules. We characterize when the skinning map has bounded image.
Yusheng Luo, Yongquan Zhang
wiley +1 more source