A general comparison theorem with applications to volume estimates for submanifolds
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 11 (1978) no. 4, pp. 451-470. 
@article{ASENS_1978_4_11_4_451_0,
     author = {Heintze, Ernst and Karcher, Hermann},
     title = {A general comparison theorem with applications to volume estimates for submanifolds},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {451--470},
     publisher = {Elsevier},
     volume = {Ser. 4, 11},
     number = {4},
     year = {1978},
     doi = {10.24033/asens.1354},
     mrnumber = {80i:53026},
     zbl = {0416.53027},
     language = {en},
     url = {http://archive.numdam.org/articles/10.24033/asens.1354/}
}
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
SP  - 451
EP  - 470
VL  - 11
IS  - 4
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.24033/asens.1354/
DO  - 10.24033/asens.1354
LA  - en
ID  - ASENS_1978_4_11_4_451_0
ER  - 
%0 Journal Article
%A Heintze, Ernst
%A Karcher, Hermann
%T A general comparison theorem with applications to volume estimates for submanifolds
%J Annales scientifiques de l'École Normale Supérieure
%D 1978
%P 451-470
%V 11
%N 4
%I Elsevier
%U http://archive.numdam.org/articles/10.24033/asens.1354/
%R 10.24033/asens.1354
%G en
%F ASENS_1978_4_11_4_451_0
Heintze, Ernst; Karcher, Hermann. A general comparison theorem with applications to volume estimates for submanifolds. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 11 (1978) no. 4, pp. 451-470. doi : 10.24033/asens.1354. http://archive.numdam.org/articles/10.24033/asens.1354/

[1] M. Berger, An Extension of Rauch's Metric Comparison Theorem and some Applications (Illinois J. Math., vol. 6, 1962, pp. 700-712). | MR | Zbl

[2] R. Bishop, A Relation Between Volume, Mean Curvature and Diameter (Amer. Math. Soc. Not., vol. 10, 1963, pp. 364).

[3] K. Borsuk, Sur la courbure totale des courbes fermées (Ann. Soc. Polon. Math., vol. 20, 1947, pp. 251-265). | MR | Zbl

[4] J. Cheeger, Finiteness theorems for Riemannian manifolds (Amer. J. Math., vol. 92, 1970, pp. 61-74). | MR | Zbl

[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). | MR | Zbl

[6] W. Fenchel, Über die Krümmung und Windung geschlossener Raumkurven (Math. Ann., vol. 101, 1929, pp. 238-252). | JFM

[7] K. Grove and K. Shiohama, A Generalized Sphere Theorem (Ann. of Math., vol. 106, 1977, pp. 201-211). | MR | Zbl

[8] C. Heim, Une borne pour la longueur des géodésiques périodiques d'une variété riemannienne compacte (Thèse, Paris, 1971).

[9] W. Klingenberg, Contribution to Riemannian Geometry in the Large (Ann. of Math., vol. 69, 1959, pp. 654-666). | MR | Zbl

[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). | MR | Zbl

[11] H. E. Rauch, A Contribution to Differential Geometry in the Large (Ann. of Math., vol. 54, 1951, pp. 38-55). | MR | Zbl

[12] F. W. Warner, The Conjugate Locus of a Riemannian Manifold (Amer. J. Math., vol. 87, 1965, pp. 575-604). | MR | Zbl

[13] F. W. Warner, Extensions of the Rauch Comparison Theorem to Submanifolds (Trans. Amer. Math. Soc., vol. 122, 1966, pp. 341-356). | MR | Zbl

[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). | Zbl

[15] T. J. Willmore, Note on Embedded Surfaces (An. Sti. Univ. “Al. I. Cuza”, Iasi, Sect. Ia Mat., 11B, 1965, pp. 493-496). | MR | Zbl

[16] W. Ziller, Closed Geodesics on Homogeneous Spaces [Math. Z. (to appear)].

Cité par Sources :