Hamiltonian stability and index of minimal Lagrangian surfaces of the complex projective plane

摘要

We show that the Cfifford torus and the totally geodesic real projective plane RP2 in the complex projective plane CP2 are the unique Hamiltonian stable minimal Lagrangian compact surfaces of CP2 with genus g <= 4, when the surface is orientable, and with Euler characteristic X <= -1, when the surface is nonorientable. Also we characterize RP2 in CP2 as the least possible index minimal Lagrangian compact nonorientable surface of CP2.