Every sub-Riemannian manifold is the Gromov–Hausdorff limit of a sequence Riemannian manifolds
Sign Up to like & getrecommendations! Published in 2017 at "Acta Mathematica Sinica, English Series"
DOI: 10.1007/s10114-017-4543-x
Abstract: In this paper, we will show that every sub-Riemannian manifold is the Gromov–Hausdorff limit of a sequence of Riemannian manifolds. read more here.
Keywords: gromov hausdorff; hausdorff limit; manifold gromov; every sub ... See more keywords
On the average L-dimensions of typical measures belonging to the Gromov–Hausdorff–Prohoroff space
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2018.09.044
Abstract: Abstract We study the average L q -dimensions of typical Borel probability measures belonging to the Gromov–Hausdorff–Prohoroff space (of all Borel probability measures with compact supports) equipped with the Gromov–Hausdorff–Prohoroff metric. read more here.
Keywords: average dimensions; dimensions typical; gromov hausdorff; hausdorff prohoroff ... See more keywords
Local structure of Gromov–Hausdorff space around generic finite metric spaces
Sign Up to like & getrecommendations! Published in 2017 at "Lobachevskii Journal of Mathematics"
DOI: 10.1134/s1995080217060038
Abstract: We investigate the local structure of the space M consisting of isometry classes of compact metric spaces, endowed with the Gromov–Hausdorff metric. We consider finite metric spaces of the same cardinality and suppose that these… read more here.
Keywords: space; gromov hausdorff; metric spaces; finite metric ... See more keywords
Gromov–Hausdorff–Prokhorov convergence of vertex cut-trees of $n$-leaf Galton–Watson trees
Sign Up to like & getrecommendations! Published in 2019 at "Bernoulli"
DOI: 10.3150/18-bej1055
Abstract: In this paper we study the vertex cut-trees of Galton-Watson trees conditioned to have $n$ leaves. This notion is a slight variation of Dieuleveut's vertex cut-tree of Galton-Watson trees conditioned to have $n$ vertices. Our… read more here.
Keywords: gromov hausdorff; watson trees; galton watson; prokhorov ... See more keywords
Gromov-Hausdorff stability of reaction diffusion equations with Robin boundary conditions under perturbations of the domain and equation
Sign Up to like & getrecommendations! Published in 2021 at "Communications on Pure and Applied Analysis"
DOI: 10.3934/cpaa.2021020
Abstract: In this paper, we prove the continuity of global attractors and the Gromov-Hausdorff stability of reaction diffusion equations with Robin boundary conditions under perturbations of the domain and equation if every equilibrium of the unperturbed… read more here.
Keywords: reaction diffusion; gromov hausdorff; hausdorff stability; diffusion equations ... See more keywords
Topological stability from Gromov-Hausdorff viewpoint
Sign Up to like & getrecommendations! Published in 2017 at "Discrete and Continuous Dynamical Systems"
DOI: 10.3934/dcds.2017151
Abstract: We combine the classical Gromov-Hausdorff metric [ 5 ] with the \begin{document}$C^0$\end{document} distance to obtain the \begin{document}$C^0$\end{document} - Gromov - Hausdorff distance between maps of possibly different metric spaces. The latter is then combined with… read more here.
Keywords: topologically stable; gromov hausdorff; stability; topological stability ... See more keywords
Gromov-Hausdorff stability for group actions
Sign Up to like & getrecommendations! Published in 2021 at "Discrete and Continuous Dynamical Systems"
DOI: 10.3934/dcds.2020320
Abstract: We will extend the topological Gromov-Hausdorff stability [ 2 ] from homeomorphisms to finitely generated actions. We prove that if an action is expansive and has the shadowing property, then it is topologically GH-stable. From… read more here.
Keywords: gromov hausdorff; hausdorff stability; stability group; group actions ... See more keywords