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 COpen image in new window ∂K with arclength s where SOpen image in new window motivates the introduction of a hyperbolic support function H of K. Hereby H(φ) Open image in new windowd(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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