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This is a joint work with Chungen Liu.In this talk,we briefly review Maslov type index theory for symplectic paths with Lagrangian boundary.As a application we prove that there exist at least n geometrically distinct brake orbits on every C2 compact convex symmetric hypersurface Σ in R2n satisfying the reversible condition NΣ = Σ with N = diag(-In,In).As a consequence,we show that if the Hamiltonian function is convex and even,then Seifert conjecture of 1948 on the multiplicity of brake orbits holds for any positive integer n.