Harmonic symmetrization of convex sets and of Finsler structures, with applications to Hilbert geometry

DOI10.1016/j.exmath.2008.10.001zbMath1166.58004arXiv0807.0335OpenAlexW2162103979MaRDI QIDQ1012900

Athanase Papadopoulos, Marc Troyanov

Publication date: 23 April 2009

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0807.0335

zbMATH Keywords

Hilbert metricFunk weak metricharmonic symmetrizationtautological Finsler structureweak Finsler structure

Mathematics Subject Classification ID

Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) General theory of distance geometry (51K05) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60) Convex sets in topological vector spaces (aspects of convex geometry) (52A07) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Local differential geometry of Finsler spaces and generalizations (areal metrics) (53B40) Synthetic differential geometry (51K10)

Related Items

Weak Finsler structures and the Funk weak metric, The Funk and Hilbert geometries for spaces of constant curvature, Weighted floating bodies and polytopal approximation, Convex bodies in Euclidean and Weil-Petersson geometries, Deforming convex projective manifolds, Plateau's problem in Finsler 3-space, Harmonic symmetrization of convex sets and of Finsler structures, with applications to Hilbert geometry

Cites Work

• Hilbert geometry for convex polygonal domains
• Hilbert metrics and Minkowski norms
• Harmonic symmetrization of convex sets and of Finsler structures, with applications to Hilbert geometry
• The Hilbert metric and Gromov hyperbolicity.
• Divisible convex sets. II
• Behaviour of distance functions in Hilbert-Finsler geometry.
• Hilbert geometry for strictly convex domains
• Divisible convex sets. IV: Boundary structure in dimension 3
• Weak Finsler structures and the Funk weak metric
• Convexes divisibles III
• Spaces with non-symmetric distance
• Local Metric Geometry
• Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8)
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