Some isoperimetric inequalities and eigenvalue estimates

Christopher B. Croke

Annales scientifiques de l'École Normale Supérieure (1980)

  • Volume: 13, Issue: 4, page 419-435
  • ISSN: 0012-9593

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Croke, Christopher B.. "Some isoperimetric inequalities and eigenvalue estimates." Annales scientifiques de l'École Normale Supérieure 13.4 (1980): 419-435. <http://eudml.org/doc/82059>.

@article{Croke1980,
author = {Croke, Christopher B.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {isoperimetric inequality; geodesic ray; first eigenvalue of the Dirichlet problem; Laplacian},
language = {eng},
number = {4},
pages = {419-435},
publisher = {Elsevier},
title = {Some isoperimetric inequalities and eigenvalue estimates},
url = {http://eudml.org/doc/82059},
volume = {13},
year = {1980},
}

TY - JOUR
AU - Croke, Christopher B.
TI - Some isoperimetric inequalities and eigenvalue estimates
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1980
PB - Elsevier
VL - 13
IS - 4
SP - 419
EP - 435
LA - eng
KW - isoperimetric inequality; geodesic ray; first eigenvalue of the Dirichlet problem; Laplacian
UR - http://eudml.org/doc/82059
ER -

References

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  1. [1] M. BERGER, Lectures on Geodesics in Riemannian Geometry, Tata Institute, Bombay, 1965. Zbl0165.55601MR35 #6100
  2. [2] M. BERGER, Some Relations Between Volume, Injectivity Radius, and Convexity Radius in Riemannian Manifolds, Differential Geometry and Relativity, D. Reidel Publishing Co., Dordrecht-Boston, 1976, pp. 33-42. Zbl0342.53038MR56 #6562
  3. [3] M. BERGER, Une inégalité universelle pour la première valeur propre du laplacien (Bull. Soc. math. Fr., T. 107, 1979, pp. 3-9). Zbl0399.35080MR80f:58046
  4. [4] A. BESSE, Manifolds All of Whose Geodesics are Closed (Ergebnisse der Mathematik, Vol. 93, Springer, Berlin-Heidelberg-New York, 1978). Zbl0387.53010MR80c:53044
  5. [5] R. BISHOP and R. CRITTENDEN, Geometry of Manifolds, Academic Press, 1964. Zbl0132.16003MR29 #6401
  6. [6] J. CHEEGER, A Lower Bound for the Smallest Eigenvalue of the Laplacian, in Problems in Analysis (A Symposium in Honor of S. Bochner, Princeton University Press, Princeton, 1970, pp. 195-199). Zbl0212.44903MR53 #6645
  7. [7] J. CHEEGER and D. G. EBIN, Comparison Theorems in Riemannian Geometry, North Holland, Amsterdam, 1975. Zbl0309.53035MR56 #16538
  8. [8] S.-Y. CHENG, On the Hayman-Osserman-Taylor Inequality (preprint). 
  9. [9] L. W. GREEN, Auf Wiedersehenflächen (Ann. of Math., Vol. 78, 1963, pp. 289-299). Zbl0116.13503MR27 #5206
  10. [10] P. LI, On the Sobolev Constant and the p-Spectrum of a Compact Riemannian Manifold (Ann. scient. Éc. Norm. Sup., T. 13, 1980, pp. 451-467). Zbl0466.53023MR82h:58054
  11. [11] R. OSSERMAN, The Isoperimetric Inequality (Bull. Amer. Math. Soc., Vol. 87, 1978, pp. 1182-1238). Zbl0411.52006MR58 #18161
  12. [12] L. A. SANTALÓ, Integral Geometry and Geometric Probability (Encyclopedia of Mathematics and Its Applications), Addison-Wesley, London-Amsterdam-Dom Mills, Ontario-Sydney-Tokyo, 1976. Zbl0342.53049MR55 #6340
  13. [13] S.-T. YAU, Isoperimetric Constants and the First Eigenvalue of a Compact Riemannian Manifold [Ann. scient. Éc. Norm. Sup., (4), T. 8, 1975, pp. 487-507]. Zbl0325.53039MR53 #1478

Citations in EuDML Documents

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  1. Marcel Berger, Une borne inférieure pour le volume d'une variété riemannienne en fonction du rayon d'injectivité
  2. Deane Yang, L p pinching and compactness theorems for compact riemannian manifolds
  3. Peter Li, On the Sobolev constant and the p -spectrum of a compact riemannian manifold
  4. Olli Martio, V. Miklyukov, M. Vuorinen, Estimates for the energy integral of quasiregular mappings on Riemannian manifolds and isoperimetry
  5. Michael Cowling, Stefano Meda, Roberta Pasquale, Riesz potentials and amalgams
  6. Vincent Minerbe, On the asymptotic geometry of gravitational instantons
  7. Deane Yang, Convergence of riemannian manifolds with integral bounds on curvature. I
  8. Francescopaolo Montefalcone, Some relations among volume, intrinsic perimeter and one-dimensional restrictions of B V functions in Carnot groups
  9. Peter Buser, A note on the isoperimetric constant
  10. Sylvestre Gallot, Finiteness theorems with integral conditions on curvature

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