Convex half-spaces
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Marek Lassak (1984)
Fundamenta Mathematicae
Moussafir, J.-O. (2000)
Zapiski Nauchnykh Seminarov POMI
Kurz, Sascha (2008)
Beiträge zur Algebra und Geometrie
H. Martini (1991)
Discrete & computational geometry
Soltan, Valeriu (2010)
Beiträge zur Algebra und Geometrie
G.R. Burton (1977)
Monatshefte für Mathematik
Yves Benoist (2003)
Publications Mathématiques de l'IHÉS
Every bounded convex open set Ω of Rm is endowed with its Hilbert metric dΩ. We give a necessary and sufficient condition, called quasisymmetric convexity, for this metric space to be hyperbolic. As a corollary, when the boundary is real analytic, Ω is always hyperbolic. In dimension 2, this condition is: in affine coordinates, the boundary ∂Ω is locally the graph of a C1 strictly convex function whose derivative is quasisymmetric.
Vladimir I. Oliker (2005)
Banach Center Publications
E. Schulte, Vrecica (1985)
Monatshefte für Mathematik
Dumitrescu, Adrian, Jiang, Minghui (2010)
Beiträge zur Algebra und Geometrie
Dalla, Leoni, Samiou, Evangelia (2007)
Beiträge zur Algebra und Geometrie
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