Results 51 to 60 of about 4,807 (127)
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
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Mass and radius of balls in Gromov-Hausdorff-Prokhorov convergent sequences
, 2022 We survey some properties of Gromov--Hausdorff--Prokhorov convergent sequences $(\mathsf{X}_n, d_{\mathsf{X}_n}, ν_{\mathsf{X}_n})_{n \ge 1}$ of random compact metric spaces equipped with Borel probability measures. We formalize that if the limit is almost surely non-atomic, then for large $n$ each open ball in $\mathsf{X}_n$ with small radius must ...
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Lorentzian Gromov-Hausdorff convergence and pre-compactness
The goal of the paper is to introduce a convergence à la Gromov-Hausdorff for Lorentzian spaces, building on $ε$-nets consisting of causal diamonds and relying only on the time separation function. This yields a geometric notion of convergence, which can be applied to synthetic Lorentzian spaces (Lorentzian pre-length spaces) or smooth spacetimes ...
Mondino, Andrea, Sämann, Clemens
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Quantum Gromov-Hausdorff Convergence for Extensions of $C^*$-Algebras
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Bhatt, Vibhor +2 more
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Quantum Gromov-Hausdorff convergence of spectral truncations for groups with polynomial growth
, 2023 For a unital spectral triple $(\mathcal{A}, H,D)$, we study when its truncation converges to itself. The spectral truncation is obtained by using the spectral projection $P_Λ$ of $D$ onto $[-Λ,Λ]$ to deal with the case where only a finite range of energy levels of a physical system is available.
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Convergence of Heisenberg modules over quantum 2-tori for the modular Gromov-Hausdorff propinquity
Journal of Operator Theory, 2020 The modular Gromov-Hausdorff propinquity is a distance on classes of modules endowed with quantum metric information, in the form of a metric form of a connection and a left Hilbert module structure. This paper proves that the family of Heisenberg modules over quantum two tori, when endowed with their canonical connections, form a continuous family for
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Gromov-Hausdorff Convergence of Spectral Truncations for Quantum Groups
We study the quantum Gromov-Hausdorff convergence of spectral truncations for compact quantum groups. Using a proper length function, we define a Dirac operator and the associated spectral truncations. This work extends the previous convergence results for tori (Leimbach-van Suijlekom) to a broad class of quantum groups, and provides Gromov-Hausdorff ...
Peng, Xintao, Wang, Qin
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Null Distance and Convergence of Lorentzian Length Spaces. [PDF]
Ann Henri Poincare, 2022 Kunzinger M, Steinbauer R.
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Cheeger constant, $p$-Laplacian, and Gromov-Hausdorff convergence
, 2013 We discuss the behavior of $(λ_{1. p}(M))^{1/p}$ with respect to the Gromov-Hausdorff topology and the variable $p$, where $λ_{1, p}(M)$ is the first positive eigenvalue of the $p$-Laplacian on a compact Riemannian manifold $M$. Applications include new estimates for the first eigenvalues of the $p$-Laplacian on Riemannian manifolds with lower Ricci ...
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Surface measure on, and the local geometry of, sub-Riemannian manifolds. [PDF]
Calc Var Partial Differ Equ, 2023 Don S, Magnani V.
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