Stability of closed characteristics on compact convex hypersurfaces in R-6

摘要

Let Sigma subset of R-6 be a compact convex hypersurface. We prove that if Sigma carries only finitely many geometrically distinct closed characteristics, then at least two of them must have irrational mean indices. Moreover, if Sigma carries exactly three geometrically distinct closed characteristics, then at least two of them must be elliptic.