Differential and Integral Equations

Smooth approximation of weak Finsler metrics

Andrea Davini

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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.

Article information

Source
Differential Integral Equations, Volume 18, Number 5 (2005), 509-530.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060183

Mathematical Reviews number (MathSciNet)
MR2136977

Zentralblatt MATH identifier
1212.41092

Subjects
Primary: 49J45: Methods involving semicontinuity and convergence; relaxation
Secondary: 53C60: Finsler spaces and generalizations (areal metrics) [See also 58B20]

Citation

Davini, Andrea. Smooth approximation of weak Finsler metrics. Differential Integral Equations 18 (2005), no. 5, 509--530. https://projecteuclid.org/euclid.die/1356060183


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