대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제12권1호
  • /
  • Pages.101-108
  • /
  • 1997
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지

Constant scalar curvature on open manifolds with finite volume

  • Kim, Seong-Tag (Department of Mathematics, Sung Kwan Kwan University)
  • 발행 : 1997.01.01
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초록

We let (M,g) be a noncompact complete Riemannina manifold of dimension $n \geq 3$ with finite volume and positive scalar curvature. We show the existence of a conformal metric with constant positive scalar curvature on (M,g) by gluing solutions of Yamabe equation on each compact subsets $K_i$ with $\cup K_i = M$ .

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참고문헌

  1. J. Math. Pures Appl. v.55 Equations differentielles non lineaires et probleme de Yamabe concernant la courbure scalaire T. Aubin
  2. Nonlinear analysis on manifolds, Monge-Ampere equations T. Aubin
  3. J. Diff. Geom. v.27 Conformal deformation to constant negative scalar curvature on noncompact Riemannian manifolds P. Aviles;R. McOwen
  4. Comm. Pure Appl. Math v.42 Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth A. Caffarelli;B. Gidas;J. Spruck
  5. Elliptic partial differential equations of second order D. Gilbarg;N. S. Trudinger
  6. Partial differential equatiions, Lect. Notes in Math. v.1306 A counterexample to the Yamabe problem for complete noncompact manifolds Z. Jin
  7. Nonliner Analysis v.26 Scalar curvature on noncompact complete Riemannian manifolds S. Kim
  8. Geometriae Dedicata (to appear) The Yamabe problem and applications on noncompact complete Riemannian manifolds S. Kim
  9. Bull. Amer. Math. Soc. v.17 The Yamabe problem L. M. Lee;T.K. Parker
  10. J. Diff. Geom. v.34 Conformally flat metrics of constant positive scalar curvature on subdomains of the sphere R. Mazzeo;N. Smale
  11. Constant scalar curvature metrics with isolated singularities R. Mazzeo;F. Pacard
  12. J. Diff. Geom. v.20 Conformal deformation of a Riemannian metric to constant scalar curvature R. Schoen
  13. Comm. Pure Appl. Math. v.41 The existence of weak solutions with prescribed singular behavior for a conformally invariant scalar equation R. Schoen
  14. Invent. Math. v.92 Conformally flat manifolds, Kleinian groups and scalar curvature R. Schoen;S. T. Yau
  15. Ann. Scuola Norm. Sup. Pisa v.3 Remarks concerning the conformal deformation of Riemannian structures on compact manifold N. S. Trudinger
  16. Osaka Math. J. v.12 On a deformation of Riemannian structures on compact manifolds H. Yamabe