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Volumn 59, Issue 2, 2009, Pages 563-573

Two generalizations of cheeger-gromoll splitting theorem via bakry-emery ricci curvature

Author keywords

Bakry emery ricci curvature; Busemann function; Splitting theorem

Indexed keywords


EID: 67149088337     PISSN: 03730956     EISSN: None     Source Type: Journal    
DOI: 10.5802/aif.2440     Document Type: Article
Times cited : (103)

References (21)
  • 1
    • 0001119849 scopus 로고
    • Diffusions hypercontractives
    • Séminaire de probabilites, XIX, 1983/84, Springer, Berlin
    • D. BAKRY & m. ÉMERY, "Diffusions hypercontractives", in Séminaire de probabilites, XIX, 1983/84, Lecture Notes in Math., vol. 1123, Springer, Berlin, 1985, p. 177-206.
    • (1985) Lecture Notes in Math , vol.1123 , pp. 177-206
    • BAKRY, D.1    ÉMERY, M.2
  • 2
    • 0002925263 scopus 로고
    • L'hypercontractivité et son utilisation en théorie des semigroupes
    • Lectures on probability theory Saint-Flour, 1992, Springer, Berlin
    • D. BAKRY, "L'hypercontractivité et son utilisation en théorie des semigroupes", in Lectures on probability theory (Saint-Flour, 1992), Lecture Notes in Math., vol. 1581, Springer, Berlin, 1994, p. 1-114.
    • (1994) Lecture Notes in Math , vol.1581 , pp. 1-114
    • BAKRY, D.1
  • 3
    • 67149123755 scopus 로고    scopus 로고
    • Volume comparison theorems without Jacobi fields
    • Current trends in potential theory, Theta, Bucharest
    • D. BAKRY & Z. QIAN, "Volume comparison theorems without Jacobi fields", in Current trends in potential theory, Theta Ser. Adv. Math., vol. 4, Theta, Bucharest, 2005, p. 115-122.
    • (2005) Theta Ser. Adv. Math , vol.4 , pp. 115-122
    • BAKRY, D.1    QIAN, Z.2
  • 4
    • 85036828656 scopus 로고    scopus 로고
    • A. L. BESSE, Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 10, Springer-Verlag, Berlin, 1987, xii+510 pages.
    • A. L. BESSE, Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 10, Springer-Verlag, Berlin, 1987, xii+510 pages.
  • 5
    • 84972529366 scopus 로고
    • An extension of E. Hopf's maximum principle with an application to Riemannian geometry
    • E. cALABI, "An extension of E. Hopf's maximum principle with an application to Riemannian geometry", Duke Math. J. 25 (1958), p. 45-56.
    • (1958) Duke Math. J , vol.25 , pp. 45-56
    • cALABI, E.1
  • 6
    • 84972500359 scopus 로고
    • The splitting theorem for manifolds of nonnegative Ricci curvature
    • J. CHEEGER & D. GROMOLL, "The splitting theorem for manifolds of nonnegative Ricci curvature", J. Differential Geometry 6 (1971/72), p. 119-128.
    • (1971) J. Differential Geometry , vol.6 , pp. 119-128
    • CHEEGER, J.1    GROMOLL, D.2
  • 7
    • 0039628706 scopus 로고    scopus 로고
    • J. eSCHENBURG & E. HEINTZE, An elementary proof of the Cheeger-Gromoll splitting theorem, Ann. Global Anal. Geom. 2 (1984), no. 2, p. 141-151.
    • J. eSCHENBURG & E. HEINTZE, "An elementary proof of the Cheeger-Gromoll splitting theorem", Ann. Global Anal. Geom. 2 (1984), no. 2, p. 141-151.
  • 8
    • 38549153690 scopus 로고    scopus 로고
    • A remark on compact Ricci solitons
    • M. FERNÁNDEZ-LÓPEZ & E. GARCÍA-RÍO, "A remark on compact Ricci solitons", Math. Ann. 340 (2008), no. 4, p. 893-896.
    • (2008) Math. Ann , vol.340 , Issue.4 , pp. 893-896
    • FERNÁNDEZ-LÓPEZ, M.1    GARCÍA-RÍO, E.2
  • 9
    • 85036801928 scopus 로고    scopus 로고
    • D. GILBARG & N. S. TRUDINGER, Elliptic partial differential equations of second order, second ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 224, Springer-Verlag, Berlin, 1983, xiii+513 pages.
    • D. GILBARG & N. S. TRUDINGER, Elliptic partial differential equations of second order, second ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 224, Springer-Verlag, Berlin, 1983, xiii+513 pages.
  • 10
    • 85036838141 scopus 로고    scopus 로고
    • M. GROMOV, Structures metriques pour les varietes riemanniennes, Textes Mathe- matiques [Mathematical Texts], 1, CEDIC, Paris, 1981, Edited by J. Lafontaine and P. Pansu, iv+152 pages.
    • M. GROMOV, Structures metriques pour les varietes riemanniennes, Textes Mathe- matiques [Mathematical Texts], vol. 1, CEDIC, Paris, 1981, Edited by J. Lafontaine and P. Pansu, iv+152 pages.
  • 11
    • 85036803182 scopus 로고    scopus 로고
    • M. GROMOV, Metric structures for Riemannian and non-Riemannian spaces, Progress in Mathematics, 152, Birkhauser Boston Inc., Boston, MA, 1999, Based on the 1981 French original [ MR0682063 (85e:53051)], With appendices by M. Katz, P. Pansu and s. Semmes, Translated from the French by Sean Michael Bates, xx+585 pages.
    • M. GROMOV, Metric structures for Riemannian and non-Riemannian spaces, Progress in Mathematics, vol. 152, Birkhauser Boston Inc., Boston, MA, 1999, Based on the 1981 French original [ MR0682063 (85e:53051)], With appendices by M. Katz, P. Pansu and s. Semmes, Translated from the French by Sean Michael Bates, xx+585 pages.
  • 12
    • 25444447987 scopus 로고    scopus 로고
    • X.-D. Li, Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds, J. Math. Pures AppJ. (9) 84 (2005), no. 10, p. 1295-1361.
    • X.-D. Li, "Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds", J. Math. Pures AppJ. (9) 84 (2005), no. 10, p. 1295-1361.
  • 13
    • 0013555422 scopus 로고
    • On extensions of Myers' theorem
    • X.-M. Li, "On extensions of Myers' theorem", Bull. London Math. Soc. 27 (1995), no. 4, p. 392-396.
    • (1995) Bull. London Math. Soc , vol.27 , Issue.4 , pp. 392-396
    • Li, X.-M.1
  • 14
    • 60849120915 scopus 로고
    • Varietes riemanniennes a tenseur C non negatif
    • A. LICHNEROWICZ, "Varietes riemanniennes a tenseur C non negatif", C. R. Acad. Sci. Paris Ser. A-B 271 (1970), p. A650-A653.
    • (1970) C. R. Acad. Sci. Paris Ser. A-B , vol.271
    • LICHNEROWICZ, A.1
  • 15
    • 0242350976 scopus 로고    scopus 로고
    • Some geometric properties of the Bakry-Emery-Ricci tensor
    • J. LOTT, "Some geometric properties of the Bakry-Emery-Ricci tensor", Comment. Math. Helv. 78 (2003), no. 4, p. 865-883.
    • (2003) Comment. Math. Helv , vol.78 , Issue.4 , pp. 865-883
    • LOTT, J.1
  • 17
    • 0031285629 scopus 로고    scopus 로고
    • Estimates for weighted volumes and applications
    • Z. QIAN, "Estimates for weighted volumes and applications", Quart. J. Math. Oxford Ser. (2) 48 (1997), no. 190, p. 235-242.
    • (1997) Quart. J. Math. Oxford Ser. (2) , vol.48 , Issue.190 , pp. 235-242
    • QIAN, Z.1
  • 18
    • 85036848649 scopus 로고    scopus 로고
    • R. SCHOEN & S.-T. YAU, Lectures on differential geometry, Conference Proceedings and Lecture Notes in Geometry and Topology, I, International Press, Cambridge, MA, 1994, Lecture notes prepared by Wei Yue Ding, Kung Ching Chang [Gong Qing Zhang], Jia Qing Zhong and Yi Chao Xu, Translated from the Chinese by Ding and S. Y. Cheng, Preface translated from the Chinese by Raising Tso, v+235 pages.
    • R. SCHOEN & S.-T. YAU, Lectures on differential geometry, Conference Proceedings and Lecture Notes in Geometry and Topology, I, International Press, Cambridge, MA, 1994, Lecture notes prepared by Wei Yue Ding, Kung Ching Chang [Gong Qing Zhang], Jia Qing Zhong and Yi Chao Xu, Translated from the Chinese by Ding and S. Y. Cheng, Preface translated from the Chinese by Raising Tso, v+235 pages.
  • 19
    • 44449116337 scopus 로고    scopus 로고
    • Comparison Geometry for the Bakry-Emery Ricci Tensor
    • arXiv:math.DG/0706.1120vl
    • G. WEI & W. C. WYLIE, "Comparison Geometry for the Bakry-Emery Ricci Tensor", arXiv:math.DG/0706.1120vl.
    • WEI, G.1    WYLIE, W.C.2
  • 20
    • 44449141156 scopus 로고    scopus 로고
    • Complete shrinking Ricci solitons have finite fundamental group
    • W. WYLIE, "Complete shrinking Ricci solitons have finite fundamental group", Proc. Amer. Math. Soc. 136 (2008), no. 5, p. 1803-1806.
    • (2008) Proc. Amer. Math. Soc , vol.136 , Issue.5 , pp. 1803-1806
    • WYLIE, W.1
  • 21
    • 0040251391 scopus 로고    scopus 로고
    • The comparison geometry of Ricci curvature
    • Math. Sci. Res. Inst. Publ, Cambridge Univ. Press, Cambridge
    • S. ZHU, "The comparison geometry of Ricci curvature", in Comparison geometry (Berkeley, CA, 1993-94), Math. Sci. Res. Inst. Publ., vol. 30, Cambridge Univ. Press, Cambridge, 1997, p. 221-262.
    • (1997) Comparison geometry (Berkeley, CA, 1993-94) , vol.30 , pp. 221-262
    • ZHU, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.