Closed Characteristics on Asymmetric Convex Hypersurfaces in R 2n and the Corresponding Pinching Conditions

In this paper, we construct first a new concrete example of asymmetric convex compact C 1,1-hypersurfaces in R 2n possessing precisely n closed characteristics. Then we prove multiplicity results on the closed characteristics on convex compact hypersurfaces in R 2n pinched by not necessarily symmetric convex compact hypersurfaces.