Eigenvalues of the laplacian of compact Riemann surfaces and minimal submanifolds

Paul C. Yang; Shing-Tung Yau

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1980)

  • Volume: 7, Issue: 1, page 55-63
  • ISSN: 0391-173X

How to cite

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Yang, Paul C., and Yau, Shing-Tung. "Eigenvalues of the laplacian of compact Riemann surfaces and minimal submanifolds." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 7.1 (1980): 55-63. <http://eudml.org/doc/83832>.

@article{Yang1980,
author = {Yang, Paul C., Yau, Shing-Tung},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {upper bound for the first eigenvalue of a Riemann surface of genus g, endowed with an arbitrary Riemannian metric},
language = {eng},
number = {1},
pages = {55-63},
publisher = {Scuola normale superiore},
title = {Eigenvalues of the laplacian of compact Riemann surfaces and minimal submanifolds},
url = {http://eudml.org/doc/83832},
volume = {7},
year = {1980},
}

TY - JOUR
AU - Yang, Paul C.
AU - Yau, Shing-Tung
TI - Eigenvalues of the laplacian of compact Riemann surfaces and minimal submanifolds
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1980
PB - Scuola normale superiore
VL - 7
IS - 1
SP - 55
EP - 63
LA - eng
KW - upper bound for the first eigenvalue of a Riemann surface of genus g, endowed with an arbitrary Riemannian metric
UR - http://eudml.org/doc/83832
ER -

References

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  1. [1] M. Berger, Sur les premières valeurs propres des variétés Riemanniennes, Compositio Math., 26 (1973), pp. 129-149. Zbl0257.53048MR316913
  2. [2] S.-Y. Cheng, Eigenvalues comparison theorems and its geometric applications, Math. Z., 143 (1975), pp. 289-297. Zbl0329.53035MR378001
  3. [3] J. Hersch, Quatre properiétés isopérimétriques de membranes sphériques homogènes, C. R. Acad. Sci. Paris, 270 (1970), pp. 1645-1648. Zbl0224.73083MR292357
  4. [4] S. Kobayashi - K. Nomizu, Foundations of Differential Geometry, Volume II. Zbl0175.48504
  5. [5] L.E. Payne - G. Polya - H.F. Weinberger, On the ratio of consecutive eigenvalues, J. Mathematical Phys., 35 (1956), pp. 289-298. Zbl0073.08203MR84696
  6. [6] S. Tanno, The first eigenvalues of the laplacian on spheres, to appear in Tôhoku Math. J. Zbl0393.53024MR538918
  7. [7] H. Urakawa: On the least positive eigenvalue of the laplacian for riemannian manifolds II, preprint. MR516196
  8. [8] S.-T. Yau, Isoperimetric constants and the first eigenvalue of a compact Riemannian manifold, Ann. Sci. École Norm. Sup., 8 (1975), pp. 487-507. Zbl0325.53039MR397619

Citations in EuDML Documents

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  1. Luca Sabatini, Estimation of vibration frequencies of linear elastic membranes
  2. A. El Soufi, S. Ilias, Le volume conforme et ses applications d'après Li et Yau
  3. Ahmad El Soufi, Saïd Ilias, Antonio Ros, Sur la première valeur propre des tores
  4. Florent Balacheff, Stéphane Sabourau, Diastolic and isoperimetric inequalities on surfaces
  5. Bruno Colbois, Le spectre du laplacien agissant sur les p - formes différentielles
  6. Bruno Colbois, Spectre conforme et métriques extrémales
  7. Zindine Djadli, Opérateurs géométriques et géométrie conforme

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