We study locally compact, locally geodesically complete, locally CAT(κ) spaces (GCBA κ-spaces). We prove a Croke-type local volume estimate only depending on the dimension of these spaces. We show that a local doubling condition, with respect to the natural measure, implies pure-dimensionality. Then we consider GCBA κ-spaces satisfying a uniform packing condition at some fixed scale r or a doubling condition at arbitrarily small scale, and prove several compactness results with respect to pointed Gromov–Hausdorff convergence. Finally, as a particular case, we study convergence and stability of Mκ-complexes with bounded geometry.

Packing and doubling in metric spaces with curvature bounded above / Cavallucci, N.; Sambusetti, A.. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 300:3(2022), pp. 3269-3314. [10.1007/s00209-021-02905-5]

Packing and doubling in metric spaces with curvature bounded above

Cavallucci N.;Sambusetti A.
2022

Abstract

We study locally compact, locally geodesically complete, locally CAT(κ) spaces (GCBA κ-spaces). We prove a Croke-type local volume estimate only depending on the dimension of these spaces. We show that a local doubling condition, with respect to the natural measure, implies pure-dimensionality. Then we consider GCBA κ-spaces satisfying a uniform packing condition at some fixed scale r or a doubling condition at arbitrarily small scale, and prove several compactness results with respect to pointed Gromov–Hausdorff convergence. Finally, as a particular case, we study convergence and stability of Mκ-complexes with bounded geometry.
2022
Curvature bounds; doubling; Gromov–Hausdorff compactness; macroscopical scalar curvature; metric simplicial complexes; packing
01 Pubblicazione su rivista::01a Articolo in rivista
Packing and doubling in metric spaces with curvature bounded above / Cavallucci, N.; Sambusetti, A.. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 300:3(2022), pp. 3269-3314. [10.1007/s00209-021-02905-5]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1605134
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