Exemples d'applications holomorphes d'indice un
Annales de l'Institut Fourier, Volume 43 (1993) no. 2, pp. 369-381.

We construct a family of hyperelliptic Riemann surfaces of varying genus provided with meromorphic maps of degree two and index one. This gives an affirmative answer to a conjecture of S. Montiel and A. Ros.

Nous construisons une famille de surfaces de Riemann hyperelliptiques, de genre variable, munies de fonctions méromorphes de degré deux et d’indice un, ce qui apporte une réponse positive à une conjecture de S. Montiel et A. Ros.

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     title = {Exemples d'applications holomorphes d'indice un},
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Souam, Rabah. Exemples d'applications holomorphes d'indice un. Annales de l'Institut Fourier, Volume 43 (1993) no. 2, pp. 369-381. doi : 10.5802/aif.1337. https://aif.centre-mersenne.org/articles/10.5802/aif.1337/

[C] S. Y. Cheng, Eigenfunctions and nodal sets, Comment. Math. Helvetici, 51 (1976), 43-55. | MR | Zbl

[FC] D. Fischer-Colbrie, On complete minimal surfaces with finite Morse index in three manifolds, Invent. Math., 82 (1985), 121-132. | MR | Zbl

[FK] H.M. Farkas and I. Kra, Riemann surfaces, Springer Verlag. | Zbl

[Ga1] S. Gallot, Inégalités isopérimétriques et analytiques sur les variétés riemanniennes, Astérisque, 163-164 (1988), 31-91. | MR | Zbl

[Ga2] S. Gallot, Minorations sur le λ1 des variétés riemanniennes, Lecture Notes in Math., 901 (1981). | Numdam | MR | Zbl

[Gu] R. Gulliver, Index and total curvature of complete minimal surfaces, Proc. Symp. Pure Math., 44 (1986), 207-211. | MR | Zbl

[La] G. Laffaille, Déterminants de laplaciens, Séminaire de Théorie Spectrale et Géométrie, Université de Grenoble, (1986), 77-84. | Numdam | MR | Zbl

[LR] J. Lopez and A. Ros, Complete minimal surfaces with index one and stable constant mean curvature surfaces, Comment. Math. Helv., 64 (1989), 34-43. | MR | Zbl

[MR] S. Montiel and A. Ros, Schrodinger operators associated to a holomorphic map, Lecture Notes in Mathematics, Springer Verlag, 1481 (1990), 147-174. | MR | Zbl

[Na] S. Nayatani, Lower bounds for the Morse index of complete minimal surfaces in euclidean 3-space, Osaka J. Math., 27 (1990), 453-464. | MR | Zbl

[OsPhSa] B. Osgood, R. Phillips and P. Sarnack, Extremals of determinants of Laplacians, J. of Funct. An., 80 (1988), 148-211. | MR | Zbl

[O] R. Osserman, A survey of minimal surfaces, Dover, New York, 1986. | MR | Zbl

[R] M. Ross, Schwarz' P and D surfaces are stable, preprint (1991).

[Ty] J. Tysk, Eigenvalue estimates with applications to minimal surfaces, Pacific J. Math., 128 (1987), 361. | MR | Zbl

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