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
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10.1512/iumj.2007.56.2818
10.1512/iumj.2007.56.2818
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Indiana Univ. Math. J. 56 (2007) 931 - 946
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