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Support function and hyperbolic plane

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Abstract.

Minkowski’s theorem ∫ C (cosh d(o, ċ) − kS) ds = 0 in the hyperbolic plane (Klein’s model) for smoothly bounded horocyclic convex bodies K with outer unit normal vector u and curvature |k| ≧ 1 of C ∂K with arclength s where S <sinh d(o, ċ) grad d(o, ċ), u> motivates the introduction of a hyperbolic support function H of K. Hereby H(φ) d(l(φ), D +(φ)) is the distance of the K-supporting distance curve D +(φ) from the line l(φ) through the origin o with the direction angle φ. – The paper deals with the representation of C, s and k by H including extremal cases and an application of Minkowski’s theorem to the characterization of circles by inequalities for their hyperbolic support function.

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  1. Universität Stuttgart, Institut für Geometrie und Topologie, Pfaffenwaldring 57, 70550, Stuttgart, Germany

    Kurt Leichtweiß

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  1. Kurt Leichtweiß
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Correspondence to Kurt Leichtweiß.

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Leichtweiß, K. Support function and hyperbolic plane. manuscripta math. 114, 177–196 (2004). https://doi.org/10.1007/s00229-004-0451-3

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  • DOI: https://doi.org/10.1007/s00229-004-0451-3

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