The first eigenvalue of the laplacian on manifolds of non-negative curvature

Isaac Chavel; Edgar A. Feldman

Compositio Mathematica (1974)

  • Volume: 29, Issue: 1, page 43-53
  • ISSN: 0010-437X

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Chavel, Isaac, and Feldman, Edgar A.. "The first eigenvalue of the laplacian on manifolds of non-negative curvature." Compositio Mathematica 29.1 (1974): 43-53. <http://eudml.org/doc/89222>.

@article{Chavel1974,
author = {Chavel, Isaac, Feldman, Edgar A.},
journal = {Compositio Mathematica},
language = {eng},
number = {1},
pages = {43-53},
publisher = {Noordhoff International Publishing},
title = {The first eigenvalue of the laplacian on manifolds of non-negative curvature},
url = {http://eudml.org/doc/89222},
volume = {29},
year = {1974},
}

TY - JOUR
AU - Chavel, Isaac
AU - Feldman, Edgar A.
TI - The first eigenvalue of the laplacian on manifolds of non-negative curvature
JO - Compositio Mathematica
PY - 1974
PB - Noordhoff International Publishing
VL - 29
IS - 1
SP - 43
EP - 53
LA - eng
UR - http://eudml.org/doc/89222
ER -

References

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  1. [1] M. Berger: Geodesics in Riemannian Geometry. Tata Inst., Bombay, 1965. Zbl0165.55601MR215258
  2. [2] M. Berger: Sue les premières valeurs propres des variétés riemannienes. Compositio Math., 26 (1973) 129-149. Zbl0257.53048MR316913
  3. [3] M. Berger, P. Gauduchon, E. Mazet: Le Spectre d'une Variété Riemanniene. Lecture Notes in Math., Springer-Verlag, 1971. [4] Zbl0223.53034MR282313
  4. [4] L. Bers, F. Johns and M. Schechter: Partial Differential Equations. Interscience Publishers, 1964. Zbl0126.00207MR163043
  5. [5] R. Bishop and R. Crittenden: Geometry of Manifolds. Academic Press, 1964. Zbl0132.16003MR169148
  6. [6] J. Cheeger: The relation between the Laplacian and diameter for manifolds of non-negative curvature. Archiv der Math., 19 (1968) 558-560. Zbl0177.50201MR238227
  7. [7] H. Courant and D. Hilbert: Methods of Mathematical Physics. Vol. 1, Interscience Publishers, 1953. Zbl0051.28802
  8. [8] N. Grossman: Two applications of the technique of length-decreasing variations. Proc. A.M.S., 18 (1967) 327-333. Zbl0168.42902MR210048
  9. [9] N. Grossman: The volume of a totally geodesic hypersurface in a pinched manifold. Pac. J. Math., 23 (1967) 257-262. Zbl0158.40201MR220221
  10. [10] J. Hersch: Quatre propriétés isoperimétriques de membranes sphérique homogènes. C.R.A.S., 270 (1970) 1645-1648. Zbl0224.73083MR292357
  11. [11] W. Klingenberg: Contributions to Riemannian geometry in the large. Ann. of Math., 69 (1959) 654-666. Zbl0133.15003MR105709
  12. [12] H. Poincare: Sur les lignes géodesiques des surfaces convexes. Trans. A.M.S., 5 (1905) 237-274. Zbl36.0669.01MR1500710JFM36.0669.01
  13. [13] W.T. Reid: A comparison theorem for self-adjoint differential equations of second order. Ann. of Math., 65 (1957) 197-202. Zbl0077.08604MR92045
  14. [14] G.N. Watson: A Treatise on the Theory of Bessel Functions. Cambridge University Press, 1944; MacMillan, 1944. Zbl0063.08184MR10746

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