A metric characterization of manifolds with boundary

Conrad Plaut

Compositio Mathematica (1992)

  • Volume: 81, Issue: 3, page 337-354
  • ISSN: 0010-437X

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Plaut, Conrad. "A metric characterization of manifolds with boundary." Compositio Mathematica 81.3 (1992): 337-354. <http://eudml.org/doc/90143>.

@article{Plaut1992,
author = {Plaut, Conrad},
journal = {Compositio Mathematica},
keywords = {bounded curvature; Hopf-Rinow Theorem},
language = {eng},
number = {3},
pages = {337-354},
publisher = {Kluwer Academic Publishers},
title = {A metric characterization of manifolds with boundary},
url = {http://eudml.org/doc/90143},
volume = {81},
year = {1992},
}

TY - JOUR
AU - Plaut, Conrad
TI - A metric characterization of manifolds with boundary
JO - Compositio Mathematica
PY - 1992
PB - Kluwer Academic Publishers
VL - 81
IS - 3
SP - 337
EP - 354
LA - eng
KW - bounded curvature; Hopf-Rinow Theorem
UR - http://eudml.org/doc/90143
ER -

References

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  2. [Be] Berestovskii, V.N.Introduction of a Riemann structure into certain metric spaces, Siberian Math. J., 16 (1975), 499-507. Zbl0325.53059MR400131
  3. [CE] Cheeger, J., and Ebin, D.G.Comparison Theorems in Riemannian Geometry, North Holland, Amsterdam, 1975. Zbl0309.53035MR458335
  4. [F] Fukaya, K.A boundary of the set of the Riemannian manifolds with bounded curvatures and diameters, J. Diff. Geo.28 (1988), 1-21. Zbl0652.53031MR950552
  5. [FY] Fukaya, K. and Yamaguchi, T.Almost non-positively curved manifolds, J. Diff. Geo.33 (1991), 67-90. Zbl0758.53024MR1085135
  6. [G] Gromov, M.Groupes of polynomial growth and expanding maps, Publ. Math. I.H.E.S. 53 (1981), 53-78. Zbl0474.20018MR623534
  7. [GLP] Gromov, M., Lafontaine, J., and Pansu, P.Structure Métrique pour les Variétés Riemanniennes, Cedic/Fernant Nathan, Paris, 1981. Zbl0509.53034MR682063
  8. [GP1] Grove, K. and Petersen, P.Bounding homotopy types by geometry, Ann. of Math.128 (1988) 195-206. Zbl0655.53032MR951512
  9. [GP2] Grove, K. and Petersen, P.Manifolds near the boundary of existence, J. Diff. Geo.33 (1991), 379-394. Zbl0729.53045MR1094462
  10. [GPW] Grove, K., Petersen, P., and Wu, J.Y.Geometric finiteness theorems via controlled topology, Invent. math.99 (1990) 205-213. Zbl0747.53033MR1029396
  11. [GW] Greene, R.E. and Wu, H.Lipschitz convergence of Riemannian manifolds, Pacific Math. J.131 (1988), 119-141. Zbl0646.53038MR917868
  12. [K] Karcher, H.Riemannian Comparison Constructions, preprint. MR1013810
  13. [N] Nikolaev, I.G.Smoothness of the metric in spaces with bilaterally bounded curvature in the sense of A. P. Aleksandrov, Siberian Math. J.24 (1983) 247-263. Zbl0547.53011
  14. [P] Peters, S.Convergence of Riemannian manifolds, Compositio Math. 62 (1987), 3-16. Zbl0618.53036MR892147
  15. [P1] Plaut, C.Almost Riemannian Spaces, J. Diff. Geo., to appear. Zbl0723.53030MR1131442
  16. [P2] Plaut, C.Metric curvature, convergence, and topological finiteness, preprint. Zbl0770.53033MR1159431
  17. [PD] Plaut, C.Riemannian Geometry of Non-Riemannian Spaces, dissertation, University of Maryland, 1989. 
  18. [R] Rinow, W.Die Innere Geometrie der Metrischen Raume, Springer-Verlag, Berlin, 1961. Zbl0096.16302MR123969

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