A general comparison theorem with applications to volume estimates for submanifolds

Ernst Heintze; Hermann Karcher

Annales scientifiques de l'École Normale Supérieure (1978)

  • Volume: 11, Issue: 4, page 451-470
  • ISSN: 0012-9593

How to cite

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Heintze, Ernst, and Karcher, Hermann. "A general comparison theorem with applications to volume estimates for submanifolds." Annales scientifiques de l'École Normale Supérieure 11.4 (1978): 451-470. <http://eudml.org/doc/82023>.

@article{Heintze1978,
author = {Heintze, Ernst, Karcher, Hermann},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {comparison theorem; volume estimates; submanifolds; compact Riemannian manifold},
language = {eng},
number = {4},
pages = {451-470},
publisher = {Elsevier},
title = {A general comparison theorem with applications to volume estimates for submanifolds},
url = {http://eudml.org/doc/82023},
volume = {11},
year = {1978},
}

TY - JOUR
AU - Heintze, Ernst
AU - Karcher, Hermann
TI - A general comparison theorem with applications to volume estimates for submanifolds
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1978
PB - Elsevier
VL - 11
IS - 4
SP - 451
EP - 470
LA - eng
KW - comparison theorem; volume estimates; submanifolds; compact Riemannian manifold
UR - http://eudml.org/doc/82023
ER -

References

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  1. [1] M. BERGER, An Extension of Rauch's Metric Comparison Theorem and some Applications (Illinois J. Math., vol. 6, 1962, pp. 700-712). Zbl0113.37003MR26 #719
  2. [2] R. BISHOP, A Relation Between Volume, Mean Curvature and Diameter (Amer. Math. Soc. Not., vol. 10, 1963, pp. 364). 
  3. [3] K. BORSUK, Sur la courbure totale des courbes fermées (Ann. Soc. Polon. Math., vol. 20, 1947, pp. 251-265). Zbl0037.23602MR10,60e
  4. [4] J. CHEEGER, Finiteness theorems for Riemannian manifolds (Amer. J. Math., vol. 92, 1970, pp. 61-74). Zbl0194.52902MR41 #7697
  5. [5] B.-Y. CHEN, On the Total Curvature of Immersed Manifolds, I : An Inequality of Fenchel-Borsuk-Willmore (Amer. J. Math., vol. 93, 1971, pp. 148-162). Zbl0209.52803MR43 #3971
  6. [6] W. FENCHEL, Über die Krümmung und Windung geschlossener Raumkurven (Math. Ann., vol. 101, 1929, pp. 238-252). Zbl55.0394.06JFM55.0394.06
  7. [7] K. GROVE and K. SHIOHAMA, A Generalized Sphere Theorem (Ann. of Math., vol. 106, 1977, pp. 201-211). Zbl0341.53029MR58 #18268
  8. [8] C. HEIM, Une borne pour la longueur des géodésiques périodiques d'une variété riemannienne compacte (Thèse, Paris, 1971). 
  9. [9] W. KLINGENBERG, Contribution to Riemannian Geometry in the Large (Ann. of Math., vol. 69, 1959, pp. 654-666). Zbl0133.15003MR21 #4445
  10. [10] T. NAGAYOSHI and Y. TSUKAMOTO, On Positively Curved Riemannian Manifolds with Bounded Volume (Tôhoku Math. J., 2nd series, vol. 25, 1973, pp. 213-218). Zbl0262.53031MR49 #11428
  11. [11] H. E. RAUCH, A Contribution to Differential Geometry in the Large (Ann. of Math., vol. 54, 1951, pp. 38-55). Zbl0043.37202MR13,159b
  12. [12] F. W. WARNER, The Conjugate Locus of a Riemannian Manifold (Amer. J. Math., vol. 87, 1965, pp. 575-604). Zbl0129.36002MR34 #8344
  13. [13] F. W. WARNER, Extensions of the Rauch Comparison Theorem to Submanifolds (Trans. Amer. Math. Soc., vol. 122, 1966, pp. 341-356). Zbl0139.15601MR34 #759
  14. [14] J. H. C. WHITEHEAD, On the Covering of a Complete Space by the Geodesics through a Point (Ann. of Math., vol. 36, 1935, pp. 679-704). Zbl0012.27802
  15. [15] T. J. WILLMORE, Note on Embedded Surfaces (An. Sti. Univ. “Al. I. Cuza”, Iasi, Sect. Ia Mat., 11B, 1965, pp. 493-496). Zbl0171.20001MR34 #1940
  16. [16] W. ZILLER, Closed Geodesics on Homogeneous Spaces [Math. Z. (to appear)]. 

Citations in EuDML Documents

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  1. Gilles Courtois, Spectre d'une variété privée d'un ɛ-tube (Conditions de Dirichlet)
  2. Daniel Meyer, Minoration de la première valeur propre non nulle du problème de Neumann sur les variétés riemanniennes à bord
  3. Sylvestre Gallot, Bornes universelles pour des invariants géométriques
  4. Alessandro Savo, A mean-value lemma and applications
  5. Vicente Miquel, Vicente Palmer, Mean curvature comparison for tubular hypersurfaces in Kähler manifolds and some applications
  6. Jean-Pierre Demailly, Thomas Peternell, Michael Schneider, Kähler manifolds with numerically effective Ricci class
  7. Sylvestre Gallot, Minorations sur le λ 1 des variétés riemanniennes
  8. Alessandro Savo, A method of symmetrization ; Applications to heat and spectral estimates
  9. Gilles Courtois, Peut-on entendre les trous d'un tambour ?
  10. Paweł G. Walczak, A finiteness theorem for Riemannian submersions

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