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 (Formula presented.) -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.
Bibliographical notePublisher Copyright:
© 2019 London Mathematical Society
- 52A38 (primary)