Multiple P-invariant closed characteristics on partially symmetric compact convex hypersurfaces in {varvec{R}}^{2n}

In this paper, let $n$ be a positive integer and $P=diag(-I_{n-kappa },I_kappa ,-I_{n-kappa },I_kappa )$ for some integer $kappa in [0, n]$ , we prove that for any compact convex hypersurface $Sigma $ in $mathbf{R}^{2n}$ with $nge 2$ there exist at least two geometrically distinct P-invariant closed characteristics on $Sigma $ , provided that $Sigma $ is P-symmetric, i.e., $xin Sigma $ implies $Pxin Sigma $ . This work is shown to extend and unify several earlier works on this subject.