Exemples d'applications holomorphes d'indice un

Rabah Souam

Annales de l'institut Fourier (1993)

  • Volume: 43, Issue: 2, page 369-381
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Souam, Rabah. "Exemples d'applications holomorphes d'indice un." Annales de l'institut Fourier 43.2 (1993): 369-381. <http://eudml.org/doc/75001>.

@article{Souam1993,
abstract = {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.},
author = {Souam, Rabah},
journal = {Annales de l'institut Fourier},
keywords = {Neumann problem; Dirichlet problem},
language = {fre},
number = {2},
pages = {369-381},
publisher = {Association des Annales de l'Institut Fourier},
title = {Exemples d'applications holomorphes d'indice un},
url = {http://eudml.org/doc/75001},
volume = {43},
year = {1993},
}

TY - JOUR
AU - Souam, Rabah
TI - Exemples d'applications holomorphes d'indice un
JO - Annales de l'institut Fourier
PY - 1993
PB - Association des Annales de l'Institut Fourier
VL - 43
IS - 2
SP - 369
EP - 381
AB - 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.
LA - fre
KW - Neumann problem; Dirichlet problem
UR - http://eudml.org/doc/75001
ER -

References

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  2. [FC] D. FISCHER-COLBRIE, On complete minimal surfaces with finite Morse index in three manifolds, Invent. Math., 82 (1985), 121-132. Zbl0573.53038MR87b:53090
  3. [FK] H.M. FARKAS and I. KRA, Riemann surfaces, Springer Verlag. Zbl0475.30001
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  5. [Ga2] S. GALLOT, Minorations sur le λ1 des variétés riemanniennes, Lecture Notes in Math., 901 (1981). Zbl0493.53034MR83g:58071
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  7. [La] G. LAFFAILLE, Déterminants de laplaciens, Séminaire de Théorie Spectrale et Géométrie, Université de Grenoble, (1986), 77-84. Zbl1002.58518MR91a:58201
  8. [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. Zbl0679.53047MR90b:53006
  9. [MR] S. MONTIEL and A. ROS, Schrodinger operators associated to a holomorphic map, Lecture Notes in Mathematics, Springer Verlag, 1481 (1990), 147-174. Zbl0744.58007MR93k:58053
  10. [Na] S. NAYATANI, Lower bounds for the Morse index of complete minimal surfaces in euclidean 3-space, Osaka J. Math., 27 (1990), 453-464. Zbl0704.53006MR91g:58051
  11. [OsPhSa] B. OSGOOD, R. PHILLIPS and P. SARNACK, Extremals of determinants of Laplacians, J. of Funct. An., 80 (1988), 148-211. Zbl0653.53022MR90d:58159
  12. [O] R. OSSERMAN, A survey of minimal surfaces, Dover, New York, 1986. Zbl0209.52901MR87j:53012
  13. [R] M. ROSS, Schwarz' P and D surfaces are stable, preprint (1991). 
  14. [Ty] J. TYSK, Eigenvalue estimates with applications to minimal surfaces, Pacific J. Math., 128 (1987), 361. Zbl0594.58018MR88i:53102

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