Averkov, Gennadiy : On the Geometry of Simplices in Minkowski Spaces

Author(s):

Averkov, Gennadiy

Title:

On the Geometry of Simplices in Minkowski Spaces

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 5, 2003

Mathematics Subject Classification:

52A21			[ Finite-dimensional Banach spaces ]
52B12			[ Special polytopes ]

Abstract:

Let $T$ be a $d$-dimensional simplex in a $d$-dimensional real normed space ($=$ Minkowski space). We introduce a special Minkowskian area-measure and Minkowskian trilinear coordinates with respect to $T,$ allowing us to study Minkowskian balls which are tangent to all hyperplanes determined by the facets of $T.$ Finally we apply the derived statements to characterize simplices having special Minkowskian properties, namely simplices with equal Minkowskian heights and simplices with medians of the same Minkowskian length.

Keywords:

simplex, triangle, equiareal simplex, Euclidean space, barycentric coordinates, barycenter, center of mass, centroid, median, Minkowski space, finite dimensional Banach space, trilinear coordinates, bisector, bisectrix, inscribed sphere, inscribed circle, inscribed ball, incenter, insphere, incircle, inball, inradius, circumscribed sphere, circumscribed ball, circumsphere, circumball, circumcenter, circumradius, excenter, exsphere, exball, exradius, tangent ball, tangent circle, reduced body, Radon curve, cross-section measures

Language:

English

Publication time:

6 / 2003