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

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

T


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 $\Bbb R^d$. 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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