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Carathéodory's Theorem and H-Convexity

✍ Scribed by V. Boltyanski; H. Martini

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
165 KB
Volume
93
Category
Article
ISSN
0097-3165

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✦ Synopsis

In 1976, V. Boltyanski introduced the functional md for compact, convex bodies. With the help of this functional, some theorems of combinatorial geometry were derived. For example, the first author obtained a Helly-type theorem, later some particular cases of the Szo kefalvi Nagy problem were resolved. Further on, exact estimates for the cardinalities of primitive fixing and hindering systems of compact, convex bodies were established, etc. In this article, we discuss the connection of the classical Carathe odory Theorem with the functional md.

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