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Volumn 64, Issue 3, 1997, Pages 373-381

The Yamabe Problem and Applications on Noncompact Complete Riemannian Manifolds

Author keywords

Complete Riemannian manifolds; Nonlinear elliptic partial differential equations; Scalar curvature; Yamabe problem

Indexed keywords


EID: 0001235337     PISSN: 00465755     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1004912228515     Document Type: Article
Times cited : (16)

References (23)
  • 1
    • 0001596880 scopus 로고
    • Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire
    • Aubin, T.: Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire, J. Math. Pures Appl. 55 (1976), 269-296.
    • (1976) J. Math. Pures Appl. , vol.55 , pp. 269-296
    • Aubin, T.1
  • 3
    • 0039001258 scopus 로고
    • A study of the singularities of solutions of a class of nonlinear elliptics partial differential equations
    • Aviles, P.: A study of the singularities of solutions of a class of nonlinear elliptics partial differential equations, Comm. Partial Differential Equations 1 (1982), 609-643.
    • (1982) Comm. Partial Differential Equations , vol.1 , pp. 609-643
    • Aviles, P.1
  • 4
    • 84972505073 scopus 로고
    • Conformal deformation to constant negative scalar curvature on noncompact Riemannian manifolds
    • Aviles, P. and McOwen, R.: Conformal deformation to constant negative scalar curvature on noncompact Riemannian manifolds, J. Differential Geom. 27 (1988), 225-239.
    • (1988) J. Differential Geom. , vol.27 , pp. 225-239
    • Aviles, P.1    McOwen, R.2
  • 5
    • 84972529366 scopus 로고
    • An extension of E. Hopf's maximum principle with an application to Riemannian geometry
    • Calabi, E.: An extension of E. Hopf's maximum principle with an application to Riemannian geometry, Duke Math. J. 25 (1958), 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
    • Cheeger, J. and Gromoll, D.: The splitting theorem for manifolds of nonnegative Ricci curvature, J. Differential Geom. 6 (1971/72), 119-128.
    • (1971) J. Differential Geom. , vol.6 , pp. 119-128
    • Cheeger, J.1    Gromoll, D.2
  • 7
    • 0002560189 scopus 로고
    • Generalized stereographic projections with prescribed scalar curvature
    • Geometry and Nonlinear Partial Differential Equations (Fayetteville, AR, 1990), Amer. Math. Soc., Providence
    • Delanoe, P.: Generalized stereographic projections with prescribed scalar curvature, Geometry and Nonlinear Partial Differential Equations (Fayetteville, AR, 1990), Contemp. Math. 127, Amer. Math. Soc., Providence 1992, pp. 17-25.
    • (1992) Contemp. Math. , vol.127 , pp. 17-25
    • Delanoe, P.1
  • 8
    • 0038530077 scopus 로고
    • A counterexample to the Yamabe problem for complete noncompact manifolds
    • S.S. Chen (ed.), Partial Differential Equations, Springer-Verlag, Berlin, New York
    • Jin, Z.: A counterexample to the Yamabe problem for complete noncompact manifolds, in: S.S. Chen (ed.), Partial Differential Equations, Lecture Notes in Math. 1306, Springer-Verlag, Berlin, New York, 1988, pp. 93-101.
    • (1988) Lecture Notes in Math. , vol.1306 , pp. 93-101
    • Jin, Z.1
  • 9
    • 0030174479 scopus 로고    scopus 로고
    • Scalar curvature on noncompact complete Riemannian manifolds
    • Kim, S.: Scalar curvature on noncompact complete Riemannian manifolds, Nonlinear Anal. 26 (1996), 1985-1993.
    • (1996) Nonlinear Anal. , vol.26 , pp. 1985-1993
    • Kim, S.1
  • 10
    • 0001399282 scopus 로고
    • Scalar curvature of a metric with unit volume
    • Kobayashi, O.: Scalar curvature of a metric with unit volume, Math. Ann. 279 (1987), 253-265.
    • (1987) Math. Ann. , vol.279 , pp. 253-265
    • Kobayashi, O.1
  • 11
    • 85030707196 scopus 로고
    • The concentration-compactness principle in the calculus of variations. the locally compact case. I and II
    • Lions, P. L.: The concentration-compactness principle in the calculus of variations. The locally compact case. I and II, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984), 109-145 and 223-283.
    • (1984) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.1 , pp. 109-145
    • Lions, P.L.1
  • 12
    • 0001294182 scopus 로고    scopus 로고
    • The concentration-compactness principle in the calculus of variations. the limit case. I and II
    • Lions, P. L.: The concentration-compactness principle in the calculus of variations. The limit case. I and II, Rev. Mat. Iberoamericana 1(1) (1985), 145-201 and (2) 45-121.
    • (1985) Rev. Mat. Iberoamericana , vol.1 , Issue.1 , pp. 145-201
    • Lions, P.L.1
  • 13
    • 0001294182 scopus 로고    scopus 로고
    • Lions, P. L.: The concentration-compactness principle in the calculus of variations. The limit case. I and II, Rev. Mat. Iberoamericana 1(1) (1985), 145-201 and (2) 45-121.
    • Rev. Mat. Iberoamericana , Issue.2 , pp. 45-121
  • 14
    • 84972528282 scopus 로고
    • Conformally flat metrics of constant positive scalar curvature on subdomains of the sphere
    • Mazzeo, R. and Smale, N.: Conformally flat metrics of constant positive scalar curvature on subdomains of the sphere, J. Differential Geom. 34 (1991), 581-621.
    • (1991) J. Differential Geom. , vol.34 , pp. 581-621
    • Mazzeo, R.1    Smale, N.2
  • 15
    • 0041980279 scopus 로고
    • Singularities and the conformal scalar curvature equation
    • I. Bakelman (ed.), Denton, TX, 1990, Marcel Dekker, New York
    • McOwen, R.: Singularities and the conformal scalar curvature equation, in: I. Bakelman (ed.), Geometric Analysis and Nonlinear Partial Differential Equations (Denton, TX, 1990), Marcel Dekker, New York, 1993, pp. 221-233.
    • (1993) Geometric Analysis and Nonlinear Partial Differential Equations , pp. 221-233
    • McOwen, R.1
  • 16
    • 84968512977 scopus 로고
    • The existence of complete Riemannian metrics
    • Nomizu, K. and Ozeki, H.: The existence of complete Riemannian metrics, Proc. Amer. Math. Soc. 12 (1961), 889-891.
    • (1961) Proc. Amer. Math. Soc. , vol.12 , pp. 889-891
    • Nomizu, K.1    Ozeki, H.2
  • 18
    • 84972506352 scopus 로고
    • Conformal deformation of a Riemannian metric to constant scalar curvature
    • Schoen, R.: Conformal deformation of a Riemannian metric to constant scalar curvature, J. Differential Geom. 20 (1984), 479-495.
    • (1984) J. Differential Geom. , vol.20 , pp. 479-495
    • Schoen, R.1
  • 19
    • 84990556252 scopus 로고
    • The existence of weak solutions with prescribed singular behavior for a conformally invariant scalar equation
    • Schoen, R.: The existence of weak solutions with prescribed singular behavior for a conformally invariant scalar equation, Comm. Pure Appl. Math. 41 (1988), 317-392.
    • (1988) Comm. Pure Appl. Math. , vol.41 , pp. 317-392
    • Schoen, R.1
  • 20
    • 0002828952 scopus 로고
    • Conformally flat manifolds, Kleinian groups and scalar curvature
    • Schoen, R. and Yau, S. T.: Conformally flat manifolds, Kleinian groups and scalar curvature, Invent. Math. 92 (1988), 47-71.
    • (1988) Invent. Math. , vol.92 , pp. 47-71
    • Schoen, R.1    Yau, S.T.2
  • 21
    • 0000471156 scopus 로고
    • Remarks concerning the conformal deformation of Riemannian structures on compact manifolds
    • Trudinger, N. S.: Remarks concerning the conformal deformation of Riemannian structures on compact manifolds, Ann. Scuola Norm. Sup. Pisa (3) 22 (1968), 265-274.
    • (1968) Ann. Scuola Norm. Sup. Pisa (3) , vol.22 , pp. 265-274
    • Trudinger, N.S.1
  • 22
    • 84972561687 scopus 로고
    • On a deformation of Riemannian structures on compact manifolds
    • Yamabe, H.: On a deformation of Riemannian structures on compact manifolds, Osaka Math. J. 12 (1960), 21-37.
    • (1960) Osaka Math. J. , vol.12 , pp. 21-37
    • Yamabe, H.1
  • 23
    • 84980178548 scopus 로고
    • Harmonic functions on complete Riemannian manifolds
    • Yau, S. T.: Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975), 201-228.
    • (1975) Comm. Pure Appl. Math. , vol.28 , pp. 201-228
    • Yau, S.T.1


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