Métricas rotacionalmente invariantes y el problema de Steklov

• Montaño Carreño, Óscar Andrés ^[1]
  1. [1] Universidad del Valle
• Localización: Integración: Temas de matemáticas, ISSN 0120-419X, Vol. 32, Nº. 2, 2014 (Ejemplar dedicado a: Revista Integración), págs. 117-128
• Idioma: español
• Títulos paralelos:
  • Rotationally invariant metrics and the Steklov problem
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    Bajo condiciones en el signo de la curvatura de Ricci, encontramos cotas para el primer valor propio de Steklov en una bola n-dimensional dotada con una métrica rotacionalmente invariante.

  • English

    Under conditions on the sign of the Ricci curvature, we find bounds for the first Steklov eigenvalue, in a n-dimensional ball endowed with a rotationally invariant metric.

• Referencias bibliográficas
  • Citas [1] Bramble J.H. and Payne L.E., “Bounds in the Neumann problem for second order uniformly elliptic operators”, Pacific J. Math. 12...
  • [2] Escobar J.F., “Topics in PDE’s and Differential Geometry”, in XII Escola de Geometria Diferencial, Goiania (Ed. da UFG), (2002), 88 p.
  • [3] Escobar J.F., “The geometry of the first non-zero Stekloff eigenvalue”, J. Funct. Anal. 150 (1997), no. 2, 544-556.
  • [4] Escobar J.F., “An isoperimetric inequality and the first Steklov eigenvalue”, J. Funct. Anal. 165 (1999), no. 1, 101-116.
  • [5] Escobar J.F., “A comparison theorem for the first non-zero Steklov eigenvalue”, J. Funct. Anal. 178 (2000), no. 1, 143-155.
  • [6] Escobar J.F., “The Yamabe problem on manifolds with boundary”, J. Differential Geom. 35 (1992), no. 1, 21-84.
  • [7] Escobar J.F., “Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature on the boundary”, Ann....
  • [8] Ilias S. and Makhoul O., “A Reilly inequality for the first Steklov eigenvalue”, Differential Geom. Appl. 29 (2011), no. 5, 699-708.
  • [9] Kuttler J.R. and Sigillito V.G., “Lower bounds for Stekloff and free membrane eigenvalues”, SIAM Review 10 (1968), 368-370.
  • [10] Montaño O.A., “The Stekloff problem for rotationally invariant metrics on the ball”, Rev. Colombiana Mat. 47 (2013), no. 2, 181-190.
  • [11] Montaño O.A., “Cota superior para el primer valor propio del problema de Steklov”, 31 (2013), no. 1, 53-58.
  • [12] Payne L.E., “Some isoperimetric inequalities for harmonic functions”, SIAM J. Math. Anal. 1 (1970), 354-359.
  • [13] Steklov V.A., “Sur les problemes fondamentaux de la physique mathematique”, Ann. Sci. École Norm 19 (1902), 445-490.
  • [14] Weinstock R., “Inequalities for a classical eigenvalue problem”, J. Rational Mech. Anal. 3 (1954), 745-753.
  • [15] Wang Q. and Xia C., “Sharp bounds for the first non-zero Steklov eigenvalues”, J. Funct. Anal 257 (2009), no. 9, 2635-2644.
  • [16] Xia C. and Wang Q., “Inequalities for the Steklov eigenvalues”, Chaos Solitons Fractals 48 (2013), 61-67.
  • [17] Xia C., “Rigidity of compact manifolds with boundary and nonnegative Ricci curvature”, Proc. Amer. Math. Soc. 125 (1997), no. 6, 1801-1806.