Convergence theorem for riemannian manifolds with boundary

Shigeru Kodani

Compositio Mathematica (1990)

  • Volume: 75, Issue: 2, page 171-192
  • ISSN: 0010-437X

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Kodani, Shigeru. "Convergence theorem for riemannian manifolds with boundary." Compositio Mathematica 75.2 (1990): 171-192. <http://eudml.org/doc/90032>.

@article{Kodani1990,
author = {Kodani, Shigeru},
journal = {Compositio Mathematica},
keywords = {Lipschitz convergence; Hausdorff convergence; cut locus of the boundary; comparison theorem},
language = {eng},
number = {2},
pages = {171-192},
publisher = {Kluwer Academic Publishers},
title = {Convergence theorem for riemannian manifolds with boundary},
url = {http://eudml.org/doc/90032},
volume = {75},
year = {1990},
}

TY - JOUR
AU - Kodani, Shigeru
TI - Convergence theorem for riemannian manifolds with boundary
JO - Compositio Mathematica
PY - 1990
PB - Kluwer Academic Publishers
VL - 75
IS - 2
SP - 171
EP - 192
LA - eng
KW - Lipschitz convergence; Hausdorff convergence; cut locus of the boundary; comparison theorem
UR - http://eudml.org/doc/90032
ER -

References

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  1. [1] Cheeger, J., Finiteness theorems for Riemannian manifolds, Amer. J. Math.92 (1970) 61-74. Zbl0194.52902MR263092
  2. [2] Cheeger, J. and Ebin, D.G., Comparison Theorems in Riemannian Geometry. North Holland, 1975. Zbl0309.53035MR458335
  3. [3] Chen, B.Y., Geometry of Submanifolds, Marcel Dekker, New York, 1973. Zbl0262.53036MR353212
  4. [4] Eschenburg, J.H., Local convexity and nonnegative curvature - Gromov's proof of sphere theorem, Invent. math.84 (1986) 507-522. Zbl0594.53034MR837525
  5. [5] Eschenburg, J.H. and O'Sullivan, J.J., Jacobi tensors and Ricci curvature, Math. Ann.252 (1980) 1-26. Zbl0423.53035MR590545
  6. [6] Greene, R. and Wu, H., Lipschitz convergence of Riemannian manifolds, Pacific. J. Math.133 (1988) 119-143. Zbl0646.53038MR917868
  7. [7] Gromov, M., Structures métriques pour les variétés riemanniennes, rédiges par J. Lafontrain et P. Pansu, Textes math., nl Cedic/Fernand-Nathan, 1981. Zbl0509.53034MR682063
  8. [8] Heintze, E. and Karcher, H., A general comparison theorem with applications to volume estimate for submanifolds, Ann. Sci. Ecole Norm. Sup.11 (1978) 451-470. Zbl0416.53027MR533065
  9. [9] Kasue, A., Applications of Laplacian and Hessian comparison theorems, Advanced Studies in Pure Math., 3, Geometry of Geodesics and Related Topics, 333-386. Zbl0578.53029MR758660
  10. [10] Katsuda, A., Gromov's convergence theorem and its application, Nagoya Math. J.100 (1985) 11-48. Zbl0587.53043MR818156
  11. [11] Lawson, H.B., The unknottedness of minimal embeddings, Invent. Math.11 (1970) 183-187. Zbl0205.52002MR287447
  12. [12] Lawson, H.B. and Michelsohn M.-L., Embedding and surrounding with positive mean curvature, Invent. Math.77 (1984) 399-419. Zbl0555.53027MR759265
  13. [13] Moore, J.D. and Schulte, T., Minimal disks and compact hypersurfaces in Euclidean space, Proc. Amer. Math. Soc.94 (1985) 151-168. Zbl0574.53038MR784186
  14. [14] Peters, S., Convergence of Riemannian manifolds, Compositio Mathematica.62 (1987) 3-16. Zbl0618.53036MR892147
  15. [15] Sakai, T., Comparison and finiteness theorems in Riemannian geometry, Advanced Studies in Pure Math., 3, Geometry of Geodesics and Related Topics, 125-181. Zbl0578.53028MR758652
  16. [16] Sha, J.P., p-convex riemannian manifolds, Invent. Math. 83 (1986) 437-447. Zbl0563.53032MR827362
  17. [17] Sha, J.P., Handlebodies and p-convexity, J. Differential Geometry.25 (1987) 353-361. Zbl0661.53028MR882828
  18. [18] Wu, H., Manifolds of partially positive curvature, Indiana Univ. Math. J.36 (1987) 525-548. Zbl0639.53050MR905609
  19. [19] Yamaguchi, T., On the lengths of stable Jacobi fields, Preprint. Zbl0703.53039MR1040536

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