Abstract
AbstractLet K ⊂ ℝn+1 be a convex body of class C2 with everywhere positive Gauss curvature. We show that there exists a positive number δ(K) such that for any δ ∈ (0, δ(K)) we have Vol(Kδ) · Vol((Kδ)*) ≥ Vol(K) · Vol(K*) ≥ Vol(Kδ) · Vol((Kδ)*), where Kδ, Kδ and K* stand for the convex floating body, the illumination body, and the polar of K, respectively. We derive a few consequences of these inequalities.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
