Metric Graph Approximations of Geodesic Spaces

Metric Graph Approximations of Geodesic Spaces

We study the question of approximating a compact geodesic metric space by metric graphs satisfying a uniform upper bound on their first Betti number. We prove that, up to a suitable multiplicative constant, Reeb graphs of distance functions to a point provide optimal approximation in the Gromov-Haus...

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Hauptverfasser: Memoli, Facundo, Okutan, Osman Berat, Wang, Qingsong
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Metric Geometry
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Zusammenfassung:We study the question of approximating a compact geodesic metric space by metric graphs satisfying a uniform upper bound on their first Betti number. We prove that, up to a suitable multiplicative constant, Reeb graphs of distance functions to a point provide optimal approximation in the Gromov-Hausdsorff sense.
DOI:10.48550/arxiv.1809.05566