Explore an advanced mathematical lecture on floating bodies and duality in spaces of constant curvature. Delve into the extension of Meyer & Werner's work on Lutwak's p-affine surface area to spherical and hyperbolic spaces. Examine how the volume derivative of the floating body of a convex body, conjugated by polarity, relates to p-affine surface area in d-dimensional Euclidean space. Investigate the generalization of this concept to spaces with constant curvature, and understand how the Euclidean result can be derived through a limiting process as space curvature approaches zero. Gain insights into this complex topic, based on joint research with Elisabeth Werner, presented by Florian Besau at the Hausdorff Center for Mathematics.