Results 41 to 50 of about 7,327 (139)

Uniqueness and non‐uniqueness for the asymptotic Plateau problem in hyperbolic space

Proceedings of the London Mathematical Society, Volume 132, Issue 1, January 2026.
Abstract We prove several results on the number of solutions to the asymptotic problem in H3$\mathbb {H}^3$. Firstly, we discuss criteria that ensure uniqueness. Given a Jordan curve Λ$\Lambda$ in the asymptotic boundary of H3$\mathbb {H}^3$, we show that uniqueness of the minimal surfaces with asymptotic boundary Λ$\Lambda$ is equivalent to uniqueness
Zheng Huang, Ben Lowe, Andrea Seppi
wiley   +1 more source

A full classification of the isometries of the class of ball‐bodies

Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 3691-3698, December 2025.
Abstract Complementing our previous results, we give a classification of all isometries (not necessarily surjective) of the metric space consisting of ball‐bodies, endowed with the Hausdorff metric. ‘Ball‐bodies’ are convex bodies which are intersections of translates of the Euclidean unit ball.
Shiri Artstein‐Avidan, Arnon Chor, Dan I. Florentin   +2 more
wiley   +1 more source

Curved Noncommutative Tori as Leibniz Quantum Compact Metric Spaces

, 2015
We prove that curved noncommutative tori, introduced by Dabrowski and Sitarz, are Leibniz quantum compact metric spaces and that they form a continuous family over the group of invertible matrices with entries in the commutant of the quantum tori in the ...
Connes A., Connes A., Dąbrowski L., Frédéric Latrémolière, Gromov M., Hausdorff F., Kantorovich L. V., Kantorovich L. V., Kerr D., Latrémolière F., Latrémolière F., Latrémolière F., Latrémolière F., Rieffel M. A., Rieffel M. A., Rieffel M. A., Rieffel M. A., Rieffel M. A., Villani C.   +18 more
core   +1 more source

Boundary representations of locally compact hyperbolic groups

Proceedings of the London Mathematical Society, Volume 131, Issue 6, December 2025.
Abstract We develop the theory of Patterson–Sullivan measures for locally compact hyperbolic groups. This theory associates to certain left‐invariant metrics on the group measures on its boundary. Next, we establish irreducibility of the resulting (unitary) Koopman representations for second countable, nonelementary, unimodular locally compact ...
Michael Glasner
wiley   +1 more source

Convergence of vector bundles with metrics of Sasaki-type

, 2011
If a sequence of Riemannian manifolds, $X_i$, converges in the pointed Gromov-Hausdorff sense to a limit space, $X_\infty$, and if $E_i$ are vector bundles over $X_i$ endowed with metrics of Sasaki-type with a uniform upper bound on rank, then a ...
B. Wilking, C.L. Terng, D. Burago, D. Gromoll, E. Boeckx, E. Musso, J. Cheeger, J. Cheeger, J. Cheeger, J. Cheeger, J. Cheeger, J. Cheeger, K. Grove, M. Benyounes, M. Gromov, M. Gromov, M.A. Rieffel, M.T. Anderson, M.T. Anderson, M.T. Kadaoui Abbassi, O. Kowalski, O. Kowalski, P. Petersen, P. Solórzano, P.J. Freyd, Pedro Solórzano, S. Kobayashi, S. Sasaki, T. Shioya, T. Yamaguchi, X. Rong   +30 more
core   +1 more source

Gromov-Hausdorff distances for dynamical systems

Discrete & Continuous Dynamical Systems - A, 2020
We study equivariant Gromov-Hausdorff distances for general continuous actions which are not necessarily isometric as Fukaya introduced. We prove that if an action is expansive and has pseudo-orbit tracing property then it is stable under our adapted equivariant Gromov-Hausdorff topology.
openaire   +3 more sources

Curvature‐dimension condition of sub‐Riemannian α$\alpha$‐Grushin half‐spaces

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract We provide new examples of sub‐Riemannian manifolds with boundary equipped with a smooth measure that satisfy the RCD(K,N)$\mathsf {RCD}(K, N)$ condition. They are constructed by equipping the half‐plane, the hemisphere and the hyperbolic half‐plane with a two‐dimensional almost‐Riemannian structure and a measure that vanishes on their ...
Samuël Borza, Kenshiro Tashiro
wiley   +1 more source

Dual spaces of geodesic currents

Journal of Topology, Volume 18, Issue 4, December 2025.
Abstract Every geodesic current on a hyperbolic surface has an associated dual space. If the current is a lamination, this dual embeds isometrically into a real tree. We show that, in general, the dual space is a Gromov hyperbolic metric tree‐graded space, and express its Gromov hyperbolicity constant in terms of the geodesic current.
Luca De Rosa, Dídac Martínez‐Granado
wiley   +1 more source

Approximating Gromov-Hausdorff distance in Euclidean space

Computational Geometry
The Gromov-Hausdorff distance $(d_{GH})$ proves to be a useful distance measure between shapes. In order to approximate $d_{GH}$ for compact subsets $X,Y\subset\mathbb{R}^d$, we look into its relationship with $d_{H,iso}$, the infimum Hausdorff distance under Euclidean isometries.
Sushovan Majhi, Jeffrey Vitter, Carola Wenk   +2 more
openaire   +2 more sources

Computing the Gromov-Hausdorff Distance for Metric Trees [PDF]

ACM Transactions on Algorithms, 2015
The Gromov-Hausdorff (GH) distance is a natural way to measure distance between two metric spaces. We prove that it is NP-hard to approximate the GH distance better than a factor of 3 for geodesic metrics on a pair of trees. We complement this result by providing a polynomial time O (min n , √
Agarwal, Pankaj K., Fox, Kyle, Nath, Abhinandan, Sidiropoulos, Anastasios, Wang, Yusu   +4 more
openaire   +3 more sources