Results 1 to 10 of about 4,757 (101)

Intrinsic Flat and Gromov-Hausdorff Convergence of Manifolds with Ricci Curvature Bounded Below. [PDF]

J Geom Anal, 2017
We show that for a noncollapsing sequence of closed, connected, oriented Riemannian manifolds with Ricci curvature bounded below and diameter bounded above, Gromov-Hausdorff convergence agrees with intrinsic flat convergence.
Matveev R, Portegies JW.
europepmc   +3 more sources

Gromov - Hausdorff Convergence and Topological Stability for Actions on Wasserstein Hyperspaces

Journal of Applied Sciences and Environmental Management
In this paper, we make use of topological stability from Gromov – Hausdorff view point to establish the Gromov – Hausdorff convergence and stability of induced actions on Wasserstein hyperspaces between maps.
M. A. Morawo, M. L. Danyaro, A. S. Bailey, K. Y. Azeez   +3 more
doaj   +2 more sources

Lorentzian metric spaces and their Gromov–Hausdorff convergence [PDF]

Letters in Mathematical Physics, 2022
We present an abstract approach to Lorentzian Gromov–Hausdorff distance and convergence, and an alternative approach to Lorentzian length spaces that does not use auxiliary “positive signature” metrics or other unobserved fields.
E. Minguzzi, S. Suhr
semanticscholar   +1 more source

Gromov–Hausdorff convergence of spectral truncations for tori [PDF]

Advances in Mathematics, 2023
We consider operator systems associated to spectral truncations of tori. We show that their state spaces, when equipped with the Connes distance function, converge in the Gromov--Hausdorff sense to the space of all Borel probability measures on the torus
M. Leimbach, W. D. Suijlekom
semanticscholar   +1 more source

Gromov–Hausdorff convergence of metric pairs and metric tuples [PDF]

Differential geometry and its applications, 2023
We study the Gromov-Hausdorff convergence of metric pairs and metric tuples and prove the equivalence of different natural definitions of this concept. We also prove embedding, completeness and compactness theorems in this setting.
Andrés Ahumada Gómez, Mauricio Che
semanticscholar   +1 more source

Isometry groups of inductive limits of metric spectral triples and Gromov–Hausdorff convergence [PDF]

Journal of the London Mathematical Society, 2023
In this paper, we study the groups of isometries and the set of bi‐Lipschitz automorphisms of spectral triples from a metric viewpoint, in the propinquity framework of Latrémolière.
J. Bassi, R. Conti, Carla Farsi, Frederic Pierre Jean Latrémolière   +3 more
semanticscholar   +1 more source

Stability and equivariant Gromov–Hausdorff convergence [PDF]

Bulletin of the London Mathematical Society, 2023
We give applications of equivariant Gromov–Hausdorff convergence in various contexts. Namely, using equivariant Gromov–Hausdorff convergence, we prove a stability result in the setting of compact finite‐dimensional Alexandrov spaces.
M. Alattar
semanticscholar   +1 more source

Ahlfors regular conformal dimension and Gromov–Hausdorff convergence [PDF]

Revista matemática iberoamericana, 2022
We prove that the Ahlfors regular conformal dimension is upper semicontinuous with respect to Gromov–Hausdorff convergence when restricted to the class of uniformly perfect, uniformly quasi-selfsimilar metric spaces. Moreover, we show the continuity of
Nicola Cavallucci
semanticscholar   +1 more source

Structural stability for scalar reaction-diffusion equations

Electronic Journal of Qualitative Theory of Differential Equations, 2023
In this paper, we prove the structural stability for a family of scalar reaction-diffusion equations. Our arguments consist of using invariant manifold theorem to reduce the problem to a finite dimension and then, we use the structural stability of Morse–
Jihoon Lee, Leonardo Pires
doaj   +1 more source

Gromov–Hausdorff convergence of state spaces for spectral truncations [PDF]

Journal of Geometry and Physics, 2020
We study the convergence aspects of the metric on spectral truncations of geometry. We find general conditions on sequences of operator system spectral triples that allows one to prove a result on Gromov-Hausdorff convergence of the corresponding state ...
W. D. Suijlekom
semanticscholar   +1 more source