Hamiltonian stability and index of minimal Lagrangian surfaces of the complex projective plane Francisco Urbano 53C4253B2553A0553D12minimal Lagrangian surfacesHamiltonian stable Lagrangian surfacesindex of minimal surfaces We show that the Clifford torus and the totally geodesic real projective plane $\mathbb{R}\mathbb{P}^2$ in the complex projective plane $\mathbb{C}\mathbb{P}^2$ are the unique Hamiltonian stable minimal Lagrangian compact surfaces of $\mathbb{C}\mathbb{P}^2$ with genus $g\leq4$, when the surface is orientable, and with Euler characteristic $\chi\geq-1$, when the surface is nonorientable. Also we characterize $\mathbb{R}\mathbb{P}^2$ in $\mathbb{C}\mathbb{P}^2$ as the least possible index minimal Lagrangian compact nonorientable surface of $\mathbb{C}\mathbb{P}^2$. Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.2818 10.1512/iumj.2007.56.2818 en Indiana Univ. Math. J. 56 (2007) 931 - 946 state-of-the-art mathematics http://iumj.org/access/