Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

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Transversals and their applications
**

**
Vladimir L. Dol'nikov, Yaroslavl State University**

One of classical problems of Convex Geometry and Combinatorial Geometry
is the existence of *m*-dimensional plane intersecting all members of
a given family of convex sets in .
Such plane is called
the *m*-transversal of the family. My talk will be devoted some results
concerning transversals and their applications. Generalizations of
Hadwiger's and Grünbaum's transversal theorems will be brought.
The notion of the transversal will be generalizated by replacing
planes (in the definition) by surfaces of some general form.
Also the notion of convexity will be generalizated by some
more general notion.

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