Meyer & Werner showed that Lutwak's p-affine surface area in d-dimensional Euclidean space arises as the volume derivative of the floating body of convex body conjugated by polarity for p = −d/(d + 2). We establish an extension of this relation in the spherical and hyperbolic space. Our
results hold in spaces of constant curvature, and we also show that the Euclidean result of Meyer & Werner can be obtained by a limiting process as the space curvature tends to zero. Based on joint work with Elisabeth Werner.
