Ulam floating bodies

We study a new construction of bodies from a given convex body in Rn which are isomorphic to (weighted) floating bodies. We establish several properties of this new construction, including its relation to p‐affine surface areas. We show that these bodies are related to Ulam’ s long‐standing floating body problem which asks whether Euclidean balls are the only bodies that can float, without turning, in any orientation.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151836/1/jlms12226_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151836/2/jlms12226.pd