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.
- Standort
-
Deutsche Nationalbibliothek Frankfurt am Main
- Umfang
-
Online-Ressource
- Sprache
-
Englisch
- Erschienen in
-
On Asymmetric Distances ; volume:1 ; number:2013 ; year:2013 ; pages:200-231
Analysis and geometry in metric spaces ; 1, Heft 2013 (2013), 200-231
- Urheber
-
Mennucci, Andrea C.G.
- DOI
-
10.2478/agms-2013-0004
- URN
-
urn:nbn:de:101:1-2024041116411384610825
- Rechteinformation
-
Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Letzte Aktualisierung
-
14.08.2025, 11:03 MESZ
Datenpartner
Deutsche Nationalbibliothek. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.
Beteiligte
- Mennucci, Andrea C.G.
Ähnliche Objekte (12)
Distances on earth's surface
On the center of distances
Spectral distances on RCD spaces
Appréciation des distances
Encyclopedia of distances
Encyclopedia of distances
Encyclopedia of distances
Table of Distances.
Appréciation des distances
Convex statistical distances
Mahalanobis distances on factor model based estimation
Further study on domains and quasihyperbolic distances
Distances on earth's surface
On the center of distances
Spectral distances on RCD spaces
Appréciation des distances
Encyclopedia of distances
Encyclopedia of distances
Encyclopedia of distances
Table of Distances.
Appréciation des distances
Convex statistical distances
Mahalanobis distances on factor model based estimation
Further study on domains and quasihyperbolic distances
Distances on earth's surface
On the center of distances
Spectral distances on RCD spaces
Appréciation des distances
Encyclopedia of distances
Encyclopedia of distances
Encyclopedia of distances
Table of Distances.
Appréciation des distances
Convex statistical distances
Mahalanobis distances on factor model based estimation