On Asymmetric Distances

Abstract: 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.

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• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: On Asymmetric Distances ; volume:1 ; number:2013 ; year:2013 ; pages:200-231 ; Analysis and geometry in metric spaces ; 1, Heft 2013 (2013), 200-231

Contributors, Places and Time

• Creator: Mennucci, Andrea C.G.

Further information

• DOI: 10.2478/agms-2013-0004
• URN: urn:nbn:de:101:1-2024041116411384610825
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.