Speaker: Valeriu Soltan, George Mason University

Title: Characteristic properties of convex quadric surfaces.

Abstract: We prove that the boundary of an n-dimensional closed convex set B in Euclidean space is a convex quadric surface if and only if the middle points of every family of parallel chords of B lie in a hyperplane. An auxiliary result states that the boundary of B is a convex quadric surface if and only if there is a point p in the interior of B such that all sections of the boundary of B by 2-dimensional planes through p are convex quadric curves. Generalizations of these statements that involve boundedly polyhedral sets are given.

Place: Science and Technology Building I, Room 242

Refreshments will be served before the talk at 3:00 p.m. in Room 222.

Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491