References
M. Berger,Sur les premières valeurs propres des variétés riemanniennes, Composito Math.26 (1973), 129–149.
M. Berger, P. Gauduchon andE. Mazet,Le spectre d’une variété riemannienne, Lecture Notes in Math. (1973).
H. I. Choi andR. Schoen,The space of minimal embeddings of a surface into a three dimensional manifold of positive Ricci curvature, Inventiones Math.81 (1985), 387–394.
M. Gromov,Metric properties of Kähler manifolds, Preprint I.H.E.S. (1993).
J. Hersch,Quatre propriétés isopérimétriques de membranes sphériques homogènes, C. R. Acad. Sci. Paris270 (1970), 1645–1648.
P. Li andS. T. Yau,A new conformal invariant and its application to the Willmore conjecture and the first eigenvalue of compact surfaces, Inventiones Math.69 (1982), 269–291.
P. Yang andS. T. Yau,Eigenvalues of the Laplacian on compact Riemannian surfaces and minimal submanifolds, Ann. Scuola Norm. Sup. Pisa7 (1980), 55–63.
Author information
Authors and Affiliations
Additional information
Research of the first author was partially supported by a grant from the European Union and of the second and the third authors by their NSF grants.
Rights and permissions
About this article
Cite this article
Bourguignon, JP., Li, P. & Yau, S.T. Upper bound for the first eigenvalue of algebraic submanifolds. Commentarii Mathematici Helvetici 69, 199–207 (1994). https://doi.org/10.1007/BF02564482
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02564482