Smooth Finsler metrics are a natural generalization of Riemannian ones and have been widely studied in the framework of differential geometry. The definition can be weakened by allowing the metric to be only Borel measurable. This generalization is necessary in view of applications, such as, for instance, optimization problems. In this paper we show that smooth Finsler metrics are dense in Borel ones, generalizing the results obtained in [15]. The case of degenerate Finsler distances is also discussed.
SMOOTH APPROXIMATION OF WEAK FINSLER METRICS / Davini, Andrea. - In: DIFFERENTIAL AND INTEGRAL EQUATIONS. - ISSN 0893-4983. - STAMPA. - 18:(2005), pp. 509-530.
SMOOTH APPROXIMATION OF WEAK FINSLER METRICS
DAVINI, ANDREA
2005
Abstract
Smooth Finsler metrics are a natural generalization of Riemannian ones and have been widely studied in the framework of differential geometry. The definition can be weakened by allowing the metric to be only Borel measurable. This generalization is necessary in view of applications, such as, for instance, optimization problems. In this paper we show that smooth Finsler metrics are dense in Borel ones, generalizing the results obtained in [15]. The case of degenerate Finsler distances is also discussed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
