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Notes on Pointed Gromov-Hausdorff Convergence
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The present article addresses to everyone who starts working with (pointed) Gromov-Hausdorff convergence. In the major part, both Gromov-Hausdorff convergence of compact and of pointed metric spaces are introduced and investigated. Moreover, the relation of sublimits occurring with pointed Gromov-Hausdorff convergence and ultralimits is discussed.
Forward citations
Cited by 3 Pith papers
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Stability of heat kernel bounds under pointed Gromov--Hausdorff convergence
A conservative, regular, strongly local Dirichlet form exists on the pointed Gromov-Hausdorff limit of spaces with uniform heat kernel estimates, and the forms converge in the Mosco sense along a subsequence.
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Cubulating Surface-by-free Groups
Surface-by-free hyperbolic groups are cubulable when the monodromy comes from a sufficiently thick tight tree of homologous curves, because the group contains an essential incompressible quasiconvex track.
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Quasi-isometric modification of Gromov-Hausdorff distance
A quasi-isometric analogue of the Gromov–Hausdorff distance is defined, shown to sit between GH and pointed-GH convergence, metrizable, and path-connected on quasi-isometry classes.
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