메뉴 건너뛰기




Volumn 16, Issue 3, 2006, Pages 535-550

Noncompact manifolds with nonnegative Ricci curvature

Author keywords

asymptotically polar; fundamental group; noncompact manifold; ray density; Ricci curvature

Indexed keywords


EID: 33748295882     PISSN: 10506926     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02922066     Document Type: Article
Times cited : (7)

References (28)
  • 1
    • 84968508874 scopus 로고
    • On complete manifolds of nonnegative Ricci curvature
    • 10.2307/1990957 1030656 0704.53032
    • U. Abresch D. Gromoll 1990 On complete manifolds of nonnegative Ricci curvature J. Amer. Math Soc. 3 355 374 10.2307/1990957 1030656 0704.53032
    • (1990) J. Amer. Math Soc. , vol.3 , pp. 355-374
    • Abresch, U.1    Gromoll, D.2
  • 2
    • 0002408575 scopus 로고
    • On the topology of complete manifolds of nonnegative Ricci curvature
    • 10.1016/0040-9383(90)90024-E
    • M. Anderson 1990 On the topology of complete manifolds of nonnegative Ricci curvature Topology 91 41 55 10.1016/0040-9383(90)90024-E
    • (1990) Topology , vol.91 , pp. 41-55
    • Anderson, M.1
  • 3
    • 84968470166 scopus 로고
    • A four-dimensional Kleinian group
    • 10.2307/2154722 1240944 0876.57020
    • B. H. Bowditch G. Mess 1994 A four-dimensional Kleinian group Trans. Amer. Math. Soc. 344 1 391 405 10.2307/2154722 1240944 0876.57020
    • (1994) Trans. Amer. Math. Soc. , vol.344 , Issue.1 , pp. 391-405
    • Bowditch, B.H.1    Mess, G.2
  • 4
    • 0001822974 scopus 로고
    • Critical points of distance functions and applications to geometry
    • Springer Berlin. 10.1007/BFb0094288
    • Cheeger, J. Critical points of distance functions and applications to geometry, inGeometric Topology: Recent Developments, Lecture Notes in Math.,1504, 1-38, Springer, Berlin, (1991).
    • (1991) Geometric Topology: Recent Developments Lecture Notes in Math , vol.1504 , pp. 1-38
    • Cheeger, J.1
  • 5
    • 0031182532 scopus 로고    scopus 로고
    • On the structure of spaces with Ricci curvature bounded below, i
    • 1484888 0902.53034
    • J. Cheeger T. Colding 1997 On the structure of spaces with Ricci curvature bounded below, I J. Diff. Geom. 46 406 480 1484888 0902.53034
    • (1997) J. Diff. Geom. , vol.46 , pp. 406-480
    • Cheeger, J.1    Colding, T.2
  • 6
    • 0001265427 scopus 로고
    • On the structure of complete manifolds of nonnegative curvature
    • 10.2307/1970819 309010
    • J. Cheeger D. Gromoll 1972 On the structure of complete manifolds of nonnegative curvature Ann. of Math. 96 413 443 10.2307/1970819 309010
    • (1972) Ann. of Math. , vol.96 , pp. 413-443
    • Cheeger, J.1    Gromoll, D.2
  • 7
    • 51649160427 scopus 로고
    • Groups of polynomial growth and expanding maps
    • 10.1007/BF02698687 623534 0474.20018
    • M. Gromov 1981 Groups of polynomial growth and expanding maps Inst. Hautes Etudes Sci. Publi. Math. 53 53 73 10.1007/BF02698687 623534 0474.20018
    • (1981) Inst. Hautes Etudes Sci. Publi. Math. , vol.53 , pp. 53-73
    • Gromov, M.1
  • 9
    • 84972536395 scopus 로고
    • Examples of complete manifolds with positive Ricci curvature
    • 816669 0583.53036
    • D. Gromoll W. Meyer 1985 Examples of complete manifolds with positive Ricci curvature J. Differential Geom. 21 195 211 816669 0583.53036
    • (1985) J. Differential Geom. , vol.21 , pp. 195-211
    • Gromoll, D.1    Meyer, W.2
  • 10
    • 0002453196 scopus 로고
    • Large time behavior of the heat equation on complete manifolds with nonnegative Ricci curvature
    • 10.2307/1971385 847950
    • P. Li 1986 Large time behavior of the heat equation on complete manifolds with nonnegative Ricci curvature Ann. of Math. 124 1 21 10.2307/1971385 847950
    • (1986) Ann. of Math. , vol.124 , pp. 1-21
    • Li, P.1
  • 11
    • 0034178899 scopus 로고    scopus 로고
    • Examples with bounded diameter growth and infinite topological type
    • 10.1215/S0012-7094-00-10232-3 1756103 01455495
    • X. Menguy 2000 Examples with bounded diameter growth and infinite topological type Duke Math. J. 102 3 403 412 10.1215/S0012-7094-00-10232-3 1756103 01455495
    • (2000) Duke Math. J. , vol.102 , Issue.3 , pp. 403-412
    • Menguy, X.1
  • 12
    • 0034288251 scopus 로고    scopus 로고
    • Examples of nonpolar limit spaces
    • 10.1353/ajm.2000.0041 1781925 0981.53019
    • X. Menguy 2000 Examples of nonpolar limit spaces Amer. J. Math. 122 5 927 937 10.1353/ajm.2000.0041 1781925 0981.53019
    • (2000) Amer. J. Math. , vol.122 , Issue.5 , pp. 927-937
    • Menguy, X.1
  • 13
    • 0034372202 scopus 로고    scopus 로고
    • Noncollapsing examples with positive Ricci curvature and infinite topological type
    • 10.1007/PL00001632 1779615 0971.53030
    • X. Menguy 2000 Noncollapsing examples with positive Ricci curvature and infinite topological type Geom. Funct. Anal. 10 3 600 627 10.1007/PL00001632 1779615 0971.53030
    • (2000) Geom. Funct. Anal. , vol.10 , Issue.3 , pp. 600-627
    • Menguy, X.1
  • 14
    • 84972530010 scopus 로고
    • A note on curvature and fundamental group
    • 232311 0162.25401
    • J. Milnor 1968 A note on curvature and fundamental group J. Differential Geom. 2 1 7 232311 0162.25401
    • (1968) J. Differential Geom. , vol.2 , pp. 1-7
    • Milnor, J.1
  • 15
    • 0041697447 scopus 로고
    • Finitely generated Kleinian groups in 3-space and 3-manifolds of infinite topological type
    • 10.2307/2154708 1250823 0828.57002
    • L. Potyagailo 1994 Finitely generated Kleinian groups in 3-space and 3-manifolds of infinite topological type Trans. Amer. Math. Soc. 344 1 57 77 10.2307/2154708 1250823 0828.57002
    • (1994) Trans. Amer. Math. Soc. , vol.344 , Issue.1 , pp. 57-77
    • Potyagailo, L.1
  • 16
    • 0003158595 scopus 로고
    • Examples of manifolds of positive Ricci curvature
    • 978078 0633.53064
    • J. P. Sha D. G. Yang 1989 Examples of manifolds of positive Ricci curvature J. Differential Geom. 29 95 103 978078 0633.53064
    • (1989) J. Differential Geom. , vol.29 , pp. 95-103
    • Sha, J.P.1    Yang, D.G.2
  • 18
    • 84968474115 scopus 로고
    • On Riemannian manifolds of nonnegative kth-Ricci curvature
    • 10.2307/2154457 1112548 0783.53026
    • Z. M. Shen 1993 On Riemannian manifolds of nonnegative kth-Ricci curvature Trans. Amer. Math. Soc. 338 289 310 10.2307/2154457 1112548 0783.53026
    • (1993) Trans. Amer. Math. Soc. , vol.338 , pp. 289-310
    • Shen, Z.M.1
  • 19
    • 0040558001 scopus 로고    scopus 로고
    • Nonnegative Ricci curvature, small linear diameter growth, and finite generation of fundamental groups
    • 1823314 1035.53045
    • C. Sormani 2000 Nonnegative Ricci curvature, small linear diameter growth, and finite generation of fundamental groups J. Differential Geom. 54 547 559 1823314 1035.53045
    • (2000) J. Differential Geom. , vol.54 , pp. 547-559
    • Sormani, C.1
  • 20
    • 0041027402 scopus 로고    scopus 로고
    • On loops representing elements of the fundamental group of a complete manifold with nonnegative Ricci curvature
    • 10.1512/iumj.2001.50.2048 1889085 1040.53043
    • C. Sormani 2001 On loops representing elements of the fundamental group of a complete manifold with nonnegative Ricci curvature Indiana Univ. Math. J. 50 4 1867 1883 10.1512/iumj.2001.50.2048 1889085 1040.53043
    • (2001) Indiana Univ. Math. J. , vol.50 , Issue.4 , pp. 1867-1883
    • Sormani, C.1
  • 21
    • 0007312609 scopus 로고    scopus 로고
    • The almost rigidity of manifolds with lower bounds on Ricci curvature and minimal volume growth
    • 1730892 0970.53024
    • C. Sormani 2000 The almost rigidity of manifolds with lower bounds on Ricci curvature and minimal volume growth Comm. Anal. Geom. 8 1 159 212 1730892 0970.53024
    • (2000) Comm. Anal. Geom. , vol.8 , Issue.1 , pp. 159-212
    • Sormani, C.1
  • 22
    • 23044527760 scopus 로고    scopus 로고
    • Hausdorff convergence and universal covers
    • 10.1090/S0002-9947-01-02802-1 1837249 1005.53035
    • C. Sormani G. Wei 2001 Hausdorff convergence and universal covers Trans. Amer. Math. Soc. 353 3585 3602 10.1090/S0002-9947-01-02802-1 1837249 1005.53035
    • (2001) Trans. Amer. Math. Soc. , vol.353 , pp. 3585-3602
    • Sormani, C.1    Wei, G.2
  • 23
    • 1342288870 scopus 로고    scopus 로고
    • Universal covers for Hausdorff limits of noncompact spaces
    • 10.1090/S0002-9947-03-03412-3 2021619 1046.53027
    • C. Sormani G. Wei 2004 Universal covers for Hausdorff limits of noncompact spaces Trans. Amer. Math. Soc. 356 3 1233 1270 10.1090/S0002-9947-03- 03412-3 2021619 1046.53027
    • (2004) Trans. Amer. Math. Soc. , vol.356 , Issue.3 , pp. 1233-1270
    • Sormani, C.1    Wei, G.2
  • 25
    • 0345759779 scopus 로고    scopus 로고
    • On the fundamental group of open manifolds with nonnegative Ricci curvature
    • 10.1142/S0252959903000463 2024985 1057.53024
    • F. Yang S. Xu Z. Wang 2003 On the fundamental group of open manifolds with nonnegative Ricci curvature Chinese Ann. Math. Ser. B 24 4 469 474 10.1142/S0252959903000463 2024985 1057.53024
    • (2003) Chinese Ann. Math. Ser. B , vol.24 , Issue.4 , pp. 469-474
    • Yang, F.1    Xu, S.2    Wang, Z.3
  • 26
    • 0010675442 scopus 로고
    • Distance nonincreasing retraction of a complete open manifold of nonnegative sectional curvature
    • 10.1007/BF00133039 982765 0668.53025
    • J. Yim 1988 Distance nonincreasing retraction of a complete open manifold of nonnegative sectional curvature Ann. Global Anal. Geom. 6 2 191 206 10.1007/BF00133039 982765 0668.53025
    • (1988) Ann. Global Anal. Geom. , vol.6 , Issue.2 , pp. 191-206
    • Yim, J.1
  • 27
    • 0034259709 scopus 로고    scopus 로고
    • On fundamental groups of manifolds of nonnegative curvature
    • 10.1016/S0926-2245(00)00030-9 1783960 0993.53018
    • B. Wilking 2000 On fundamental groups of manifolds of nonnegative curvature Differential Geom. Appl. 13 129 165 10.1016/S0926-2245(00)00030-9 1783960 0993.53018
    • (2000) Differential Geom. Appl. , vol.13 , pp. 129-165
    • Wilking, B.1
  • 28
    • 84968508677 scopus 로고
    • Examples of complete manifolds of positive Ricci curvature with nilpotent isometry groups
    • 10.1090/S0273-0979-1988-15653-4 940494 0649.53024
    • G. Wei 1988 Examples of complete manifolds of positive Ricci curvature with nilpotent isometry groups Bull. Amer. Math. Soc. 19 311 313 10.1090/S0273-0979-1988-15653-4 940494 0649.53024
    • (1988) Bull. Amer. Math. Soc. , vol.19 , pp. 311-313
    • Wei, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.