This is a ioint work with Chungen Liu.In this talk,we briefly review Malsov type index theory for symplectic pahts 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 R2 satisfying the reversible condition N Σ=Σ with N = diag (-In,In).As a consequence,we show that that if the Hamiltonian function is convex and even,then the Seifert conjecture of 1948 on the multiplicity of brake orbits holds for any positive integer n.