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

top

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

top
  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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.