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The Floating Body Problem
Author(s) -
Stancu A.
Publication year - 2006
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609306018728
Subject(s) - mathematics , homothetic transformation , convex body , affine transformation , regular polygon , ellipsoid , class (philosophy) , boundary (topology) , mathematics subject classification , pure mathematics , curvature , mathematical analysis , combinatorics , geometry , convex optimization , physics , astronomy , artificial intelligence , computer science
Let K be a convex body with boundary of class C ⩾4 . We prove that, for a sufficiently small δ, the floating body K δ is homothetic to K if and only if K is an ellipsoid. The proof relies on properties of the affine curvature flow. 2000 Mathematics Subject Classification 52A20 (primary), 52A38 (secondary).