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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Bakolas, Efstathios 2014. Decentralized spatial partitioning for multi-vehicle systems in spatiotemporal flow-field. Automatica, Vol. 50, Issue. 9, p. 2389.

    Overath, Patrick and von der Mosel, Heiko 2014. Plateau’s problem in Finsler 3-space. Manuscripta Mathematica, Vol. 143, Issue. 3-4, p. 273.

    Bakolas, Efstathios 2013. 2013 American Control Conference. p. 2509.

    Papadopoulos, Athanase and Yamada, Sumio 2013. The Funk and Hilbert geometries for spaces of constant curvature. Monatshefte für Mathematik, Vol. 172, Issue. 1, p. 97.

    GAUBERT, STÉPHANE and VIGERAL, GUILLAUME 2012. A maximin characterisation of the escape rate of non-expansive mappings in metrically convex spaces. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 152, Issue. 02, p. 341.

  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 147, Issue 2
  • September 2009, pp. 419-437

Weak Finsler structures and the Funk weak metric

  • DOI:
  • Published online: 01 September 2009

We discuss general notions of metrics and of Finsler structures which we call weak metrics and weak Finsler structures. Any convex domain carries a canonical weak Finsler structure, which we call its tautological weak Finsler structure. We compute distances in the tautological weak Finsler structure of a domain and we show that these are given by the so-called Funk weak metric. We conclude the paper with a discussion of geodesics, of metric balls, of convexity, and of rigidity properties of the Funk weak metric.

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[2]J. C. Álvarez Paiva Some problems in Finsler geometry, in: Handbook of Differential Geometry. Vol. II, 133 (Elsevier, 2006).

[4]D. Bao , S. S. Chern and Z. Shen An introduction to Riemann-Finsler geometry. Graduate Texts in Mathematics (Springer Verlag, 2000).

[7]H. Busemann Local metric geometry. Trans. Amer. Math. Soc. 56 (1944), 200274.

[12]P. Funk Über geometrien, bei denen die geraden die kürzesten sind. Math. Ann. 101 (1929), 226237.

[17]A. Papadopoulos and M. Troyanov Harmonic symmetrization of convex sets and of Finsler structures, with applications to Hilbert geometry. Expo. Math. 27 (2009), 109124.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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