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.