A geometric property of the boundary of symmetric convex bodies and convexity of flotation surfaces

Convex bodies and norms associated to convex measures

“…An affirmative answer to this question was given by Meyer and Reisner in [32], and independently by K. Ball with a different proof. K. Ball's argument covers the case of an arbitrary log-concave probability measure and is described in [33].…”

“…As we have mentioned, by a theorem of Meyer-Reisner and Ball [32,33], in the log-concave case, for any δ ∈ (0, 1 2 ),…”

The central limit problem for convex bodies

“…Lemma 3 below is closely related to the so-called "convexity of the floating body", which was proved simultaneously by Meyer and Reisner [8] and by the second-named author. We shall use the latter's argument, but the difference here is that the earlier proofs involved slabs of fixed volume, whereas here we fix the slab width.…”

New higher-order equiaffine invariants

“…Therefore we should emphasize that it is precisely the convex floating body which is used in this paper. For an arbitrary convex body K, it is however true that if its floating body is convex, then it coincides with its convex floating body, see [20].…”