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.
|Titolo:||On Asymmetric Distances|
|Data di pubblicazione:||2013|
|Parole Chiave:||Asymmetric metric; length structure|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.2478/agms-2013-0004|
|Appare nelle tipologie:||1.1 Articolo in rivista|