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Abstract:

We study the Hn-Yamabe constants of Riemannian products (Formula presented.), where (M,g) is a compact Riemannian manifold of constant scalar curvature and (Formula presented.) is the hyperbolic metric on Hn. Numerical calculations can be carried out due to the uniqueness of (positive, finite energy) solutions of the equation Δu−λu+uq=0 on hyperbolic space Hn under appropriate bounds on the parameters λ,q, as shown by G. Mancini and K. Sandeep. We do explicit numerical estimates in the cases (n,m)=(2,2), (2,3), and (3,2). © 2014, Mathematica Josephina, Inc.

Registro:

Documento: Artículo
Título:On Yamabe Constants of Products with Hyperbolic Spaces
Autor:Henry, G.; Petean, J.
Filiación:Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria, Pab. I, Buenos Aires, C1428EHA, Argentina
CIMAT, A.P. 402, Guanajuato. Gto, 36000, Mexico
Palabras clave:Hyperbolic spaces; Riemannian products; Yamabe constants
Año:2015
Volumen:25
Número:2
Página de inicio:1387
Página de fin:1400
DOI: http://dx.doi.org/10.1007/s12220-014-9473-6
Título revista:Journal of Geometric Analysis
Título revista abreviado:J Geom Anal
ISSN:10506926
CODEN:JGANE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10506926_v25_n2_p1387_Henry

Referencias:

  • Akutagawa, K., Botvinnik, B., Yamabe metrics on cylindrical manifolds (2003) Geom. Funct. Anal., 13 (2), pp. 259-333
  • Akutagawa, K., Florit, L., Petean, J., On Yamabe constants of Riemannian products (2007) Commun. Anal. Geom., 15 (5), pp. 947-969
  • Ammann, B., Dahl, M., Humbert, E., Smooth Yamabe invariant and surgery (2013) J. Differ. Geom., 94 (1), pp. 1-58
  • arXiv:1204.1197, Ammann, B., Dahl, M., Humbert, E.: Low dimensional surgery and the Yamabe invariant. To appear in J. Math. Soc. Jpn; Ammann, B., Dahl, M., Humbert, E., Square-integrability of solutions of the Yamabe equation (2013) Commun. Anal. Geom., 21 (5), pp. 891-916
  • Aubin, T., (1998) Some Nonlinear Problems in Riemannian Geometry, , Springer Monographs in Mathematics, Springer, Berlin:
  • arXiv:1206.0610, Große, N., Nardmann, M.: The Yamabe constant of noncompact manifolds. To appear in J. Geom. Anal; Mancini, G., Sandeep, K., On a semilinear elliptic equation in H n (2008) Ann. Scuola Norm. Super. Pisa, 7, pp. 635-671
  • Ruiz, J.M., Results on the existence of the Yamabe minimizer of (2012) J. Geom. Phys., 62 (1), pp. 11-20
  • Schoen, R., Yau, S.T., Conformally flat manifolds, Kleinian groups and scalar curvature (1988) Invent. Math., 92 (1), pp. 47-71

Citas:

---------- APA ----------
Henry, G. & Petean, J. (2015) . On Yamabe Constants of Products with Hyperbolic Spaces. Journal of Geometric Analysis, 25(2), 1387-1400.
http://dx.doi.org/10.1007/s12220-014-9473-6
---------- CHICAGO ----------
Henry, G., Petean, J. "On Yamabe Constants of Products with Hyperbolic Spaces" . Journal of Geometric Analysis 25, no. 2 (2015) : 1387-1400.
http://dx.doi.org/10.1007/s12220-014-9473-6
---------- MLA ----------
Henry, G., Petean, J. "On Yamabe Constants of Products with Hyperbolic Spaces" . Journal of Geometric Analysis, vol. 25, no. 2, 2015, pp. 1387-1400.
http://dx.doi.org/10.1007/s12220-014-9473-6
---------- VANCOUVER ----------
Henry, G., Petean, J. On Yamabe Constants of Products with Hyperbolic Spaces. J Geom Anal. 2015;25(2):1387-1400.
http://dx.doi.org/10.1007/s12220-014-9473-6