NICOLA CAVALLUCCI

PhD Graduate

PhD program:: XXXIII


supervisor: G. Mondello
advisor: A. Sambusetti

Thesis title: Packing conditions in metric spaces with curvature bounded above and their applications

We consider metric spaces with a synthetic notion of upper curvature bound (locally CAT(k) spaces, convex spaces and Gromov-hyoerbolic spaces). As a weak and synthetic version of lower bound on the curvature we consider a uniform packing condotion at a fixed scale. We will see how this property can be expressed in terms of upper bounds of dimension and volume of balls in the locally CAT(k) radius. Moreover it implies a quantified version of the Tits alternative on convex, Gromov-hyoerbolic metric spaces. Finally it is at the base of the equivalences between several asymptotic notions such as the covering entropy and the Minkowski dimension of the boundary

Research products

11573/1689839 - 2024 - Thin actions on CAT(0) spaces
Cavallucci, Nicola; Sambusetti, Andrea - 01a Articolo in rivista
paper: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE (Pisa: Scuola Normale Superiore) pp. - - issn: 2036-2145 - wos: (0) - scopus: (0)

11573/1707004 - 2024 - Discrete groups of packed, non-positively curved, Gromov hyperbolic metric spaces
Cavallucci, Nicola; Sambusetti, Andrea - 01a Articolo in rivista
paper: GEOMETRIAE DEDICATA (Kluwer Academic Publishers:Journals Department, PO Box 322, 3300 AH Dordrecht Netherlands:011 31 78 6576050, EMAIL: frontoffice@wkap.nl, kluweronline@wkap.nl, INTERNET: http://www.kluwerlaw.com, Fax: 011 31 78 6576254) pp. 2-52 - issn: 0046-5755 - wos: WOS:001151071800001 (4) - scopus: (0)

11573/1605134 - 2022 - Packing and doubling in metric spaces with curvature bounded above
Cavallucci, N.; Sambusetti, A. - 01a Articolo in rivista
paper: MATHEMATISCHE ZEITSCHRIFT (Springer Verlag Germany:Tiergartenstrasse 17, D 69121 Heidelberg Germany:011 49 6221 3450, EMAIL: g.braun@springer.de, INTERNET: http://www.springer.de, Fax: 011 49 6221 345229) pp. 3269-3314 - issn: 0025-5874 - wos: WOS:000718722900001 (5) - scopus: 2-s2.0-85119067532 (3)

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