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Abstract:

We consider the conformal class of the Riemannian product g0+g, where g0 is the constant curvature metric on Sm and g is a metric of constant scalar curvature on some closed manifold. We show that the number of metrics of constant scalar curvature in the conformal class grows at least linearly with respect to the square root of the scalar curvature of g. This is obtained by studying radial solutions of the equation Δu -λ λu + λup = 0 on Sm and the number of solutions in terms of λ. © 2010 American Mathematical Society.

Registro:

Documento: Artículo
Título:Metrics of constant scalar curvature conformal to riemannian products
Autor:Petean, J.
Filiación:Centro De Investigación en Matemáticas, A.P. 402, 36000, Guanajuato, Guanajuato, Mexico
Departamento De Matemáticas, Facultad De Ciencias Exactas y Naturales, Universidad De Buenos Aires, Buenos Aires, Argentina
Año:2010
Volumen:138
Número:8
Página de inicio:2897
Página de fin:2905
DOI: http://dx.doi.org/10.1090/S0002-9939-10-10293-7
Título revista:Proceedings of the American Mathematical Society
Título revista abreviado:Proc. Am. Math. Soc.
ISSN:00029939
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v138_n8_p2897_Petean

Referencias:

  • Akutagawa, K., Florit, L., Petean, J., On Yamabe constants of Riemannian products (2007) Comm. Anal. Geom., 15, pp. 947-969. , MR2403191 (2009i:53030)
  • Aubin, T., Equations differentielles non-lineaires et probleme de Yamabe concernant la courbure scalaire (1976) J. Math. Pures Appl., 55, pp. 269-296. , MR0431287 (55:4288)
  • Brendle, S., Blow-up phenomena for the Yamabe equation (2008) Journal Amer. Math. Soc., 21, pp. 951-979. , MR2425176 (2009m:53084)
  • Caffarelli, A., Gidas, B., Spruck, J., Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth (1989) Comm. Pure. Appl. Math., 42, pp. 271-297. , MR982351 (90c:35075)
  • Gidas, B., Ni, W.M., Nirenberg, L., Symmetry and related properties via the maximum principle (1979) Comm. Math. Phys., 68, pp. 209-243. , MR544879 (80h:35043)
  • Gidas, B., Ni, W.M., Nirenberg, L., Symmetry of positive solutions of nonlinear elliptic equations in R n (1981) Advances in Math. Studies, 7 A, pp. 369-402. , MR634248 (84a:35083)
  • Hebey, E., Vaugon, M., Meilleures constantes dans le theoreme dinclusion de Sobolev et multiplicite pour les problemes de Nirenberg et Yamabe (1992) Indiana Univ. Math. J., 41, pp. 377-407. , MR1183349 (93m:58121)
  • Ince, E.L., (1956) Ordinary Differential Equations, , Dover Publications, New York, MR0010757 (6:65f)
  • Kobayashi, O., (1985) On the Large Scalar Curvature, , Research Report 11, Dept. Math., Keio Univ
  • Kobayashi, O., Scalar curvature of a metric with unit volume (1987) Math. Ann., 279, pp. 253-265. , MR919505 (89a:53048)
  • Kwong, M.K., Uniqueness of positive solutions of Δu - u + up = 0 in Rn (1989) Arch. Rational Mech. Analysis, 105, pp. 243-266. , MR969899 (90d:35015)
  • Obata, M., The conjectures on conformal transformations of Riemannian manifolds (1971) J. Diff. Geom., 6, pp. 247-258. , MR0303464 (46:2601)
  • Pollack, D., Nonuniqueness and high energy solutions for a conformally invariant scalar equation (1993) Comm. Anal. Geom., 1, pp. 347-414. , MR1266473 (94m:58051)
  • Schoen, R., Conformal deformation of a Riemannian metric to constant scalar curvature (1984) J. Differential Geometry, 20, pp. 479-495. , MR788292 (86i:58137)
  • Schoen, R., Variational theory for the total scalar curvature functional for Riemannian metrics and related topics (1989) Lectures Notes in Math., 1365, pp. 120-154. , Springer-Verlag, Berlin, MR994021 (90g:58023)
  • Trudinger, N., Remarks concerning the conformal deformation of Riemannian structures on compact manifolds (1968) Ann. Scuola Norm. Sup. Pisa, 22, pp. 265-274. , MR0240748 (39:2093)
  • Yamabe, H., On a deformation of Riemannian structures on compact manifolds (1960) Osaka Math. J., 12, pp. 21-37. , MR0125546 (23:A2847)

Citas:

---------- APA ----------
(2010) . Metrics of constant scalar curvature conformal to riemannian products. Proceedings of the American Mathematical Society, 138(8), 2897-2905.
http://dx.doi.org/10.1090/S0002-9939-10-10293-7
---------- CHICAGO ----------
Petean, J. "Metrics of constant scalar curvature conformal to riemannian products" . Proceedings of the American Mathematical Society 138, no. 8 (2010) : 2897-2905.
http://dx.doi.org/10.1090/S0002-9939-10-10293-7
---------- MLA ----------
Petean, J. "Metrics of constant scalar curvature conformal to riemannian products" . Proceedings of the American Mathematical Society, vol. 138, no. 8, 2010, pp. 2897-2905.
http://dx.doi.org/10.1090/S0002-9939-10-10293-7
---------- VANCOUVER ----------
Petean, J. Metrics of constant scalar curvature conformal to riemannian products. Proc. Am. Math. Soc. 2010;138(8):2897-2905.
http://dx.doi.org/10.1090/S0002-9939-10-10293-7