Approximation on Slices in Balanced Strictly Convex Domains with $$C^{2}$$ boundary

Abstract

AbstractWe show that a maximum modulus set K in a bounded strictly convex balanced domain $$\Omega $$ Ω with $$C^{2}$$ C 2 boundary can have a Lebesgue measure almost full on all slices. Additionally K has a so called slice continuity property.