Analysis and Probability Seminar- October 27, 2015

Tuesday, October 27, 2015 (3:00 p.m. in Yost 306)

Title: The Floating Body in Real Space Forms

Speaker: Florian Besau (Lecturer, Department of Mathematics, Applied Mathematics, & Statistics, Case Western Reserve University)

Abstract: The notion of convex floating body of a Euclidean convex body has recently been extended to the Euclidean unit sphere. We will present an extension to the hyperbolic setting and give a unifying approach. Thus a complete description of floating bodies in real space forms, that is, manifolds with constant curvature, is obtained.

Differentiation of the volume of the floating body gives rise to the floating area. In the Euclidean setting the floating area is better known as affine surface area. It is a classical and powerful tool in the (equi-)affine geometry of convex bodies. The floating area can be seen as a real analytic extension of the affine surface area.

This is joint work with Elisabeth Werner.

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