On Asymmetric Distances

• Autorzy: Andrea C.G. Mennucci
• Języki publikacji: EN

Abstrakty

EN

In this paper we discuss asymmetric length structures and asymmetric metric spaces. A length structure induces a (semi)distance function; by using the total variation formula, a (semi)distance function induces a length. In the first part we identify a topology in the set of paths that best describes when the above operations are idempotent. As a typical application, we consider the length of paths defined by a Finslerian functional in Calculus of Variations. In the second part we generalize the setting of General metric spaces of Busemann, and discuss the newly found aspects of the theory: we identify three interesting classes of paths, and compare them; we note that a geodesic segment (as defined by Busemann) is not necessarily continuous in our setting; hence we present three different notions of intrinsic metric space.

Słowa kluczowe

EN

Asymmetric metric; general metric; quasi metric; ostensible metric; Finsler metric; run–continuity; intrinsic metric; pathmetric; length structure

Kategorie tematyczne

• 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions
• 46B85: Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science
• 54C20: Extension of maps

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2013
• Tom: 1
• Strony: 200-231

Daty

otrzymano

2013-03-24

zaakceptowano

2013-05-15

online

2013-06-11

Twórcy

autor

Andrea C.G. Mennucci

• Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy

Bibliografia

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Identyfikatory

DOI

10.2478/agms-2013-0004