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.
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.
@article{AIF_1993__43_2_369_0, author = {Souam, Rabah}, title = {Exemples d'applications holomorphes d'indice un}, journal = {Annales de l'Institut Fourier}, pages = {369--381}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {43}, number = {2}, year = {1993}, doi = {10.5802/aif.1337}, zbl = {0788.30037}, mrnumber = {1220275}, language = {fr}, url = {http://www.numdam.org/articles/10.5802/aif.1337/} }
TY - JOUR AU - Souam, Rabah TI - Exemples d'applications holomorphes d'indice un JO - Annales de l'Institut Fourier PY - 1993 SP - 369 EP - 381 VL - 43 IS - 2 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.1337/ DO - 10.5802/aif.1337 LA - fr ID - AIF_1993__43_2_369_0 ER -
Souam, Rabah. Exemples d'applications holomorphes d'indice un. Annales de l'Institut Fourier, Tome 43 (1993) no. 2, pp. 369-381. doi : 10.5802/aif.1337. http://www.numdam.org/articles/10.5802/aif.1337/
[C] Eigenfunctions and nodal sets, Comment. Math. Helvetici, 51 (1976), 43-55. | MR | Zbl
,[FC] On complete minimal surfaces with finite Morse index in three manifolds, Invent. Math., 82 (1985), 121-132. | MR | Zbl
,[FK] Riemann surfaces, Springer Verlag. | Zbl
and ,[Ga1] Inégalités isopérimétriques et analytiques sur les variétés riemanniennes, Astérisque, 163-164 (1988), 31-91. | Numdam | MR | Zbl
,[Ga2] Minorations sur le λ1 des variétés riemanniennes, Lecture Notes in Math., 901 (1981). | Numdam | MR | Zbl
,[Gu] Index and total curvature of complete minimal surfaces, Proc. Symp. Pure Math., 44 (1986), 207-211. | MR | Zbl
,[La] Déterminants de laplaciens, Séminaire de Théorie Spectrale et Géométrie, Université de Grenoble, (1986), 77-84. | Numdam | MR | Zbl
,[LR] Complete minimal surfaces with index one and stable constant mean curvature surfaces, Comment. Math. Helv., 64 (1989), 34-43. | MR | Zbl
and ,[MR] Schrodinger operators associated to a holomorphic map, Lecture Notes in Mathematics, Springer Verlag, 1481 (1990), 147-174. | MR | Zbl
and ,[Na] Lower bounds for the Morse index of complete minimal surfaces in euclidean 3-space, Osaka J. Math., 27 (1990), 453-464. | MR | Zbl
,[OsPhSa] Extremals of determinants of Laplacians, J. of Funct. An., 80 (1988), 148-211. | MR | Zbl
, and ,[O] A survey of minimal surfaces, Dover, New York, 1986. | MR | Zbl
,[R] Schwarz' P and D surfaces are stable, preprint (1991).
,[Ty] Eigenvalue estimates with applications to minimal surfaces, Pacific J. Math., 128 (1987), 361. | MR | Zbl
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