Abstract. Several affirmative answers are given in any dimension for Ulam's question about bodies floating stable in every direction if the body floats like a ball and its floating body is spherical.

DOI: 10.14232/actasm-014-801-8

AMS Subject Classification (1991): 53C65

Keyword(s): floating body, sections, caps, weight, ball, sphere, isoperimetric inequality

Received June 23, 2014, and in final form March 7, 2015. (Registered under 51/2014.)