0 es la curvatura media sobre ∂M y v1 es el primer valor propio del problema de Steklov, entonces v1 ≥ h.]]>
0 is the mean curvature on ∂M and v1 is the first eigenvalue of the Steklov problem, then v1 ≥ h.]]>
El problema de Steklov sobre el cono
ÓSCAR ANDRÉS MONTAÑO
Universidad del Valle, Departamento de Matemáticas, Cali, Colombia.
Dedicado a Rafael Isaacs, a quien recuerdo siempre con mucho cariño e
infinita gratitud por su valioso aporte en mi formación académica.
Resumen. Sea (Mn, g) un cono de altura 0 ≤ xn+1 ≤ 1 en ℝn+1, dotado con una métrica rotacionalmente invariante 2ds2 + ƒ2(s)dw2, donde dw2 representa la métrica estándar sobre Sn-1, la esfera unitaria (n - 1)-dimensional. Supongamos que Ric(g) ≥ 0. En este artículo demostramos que si h > 0 es la curvatura media sobre ∂M y v1 es el primer valor propio del problema de Steklov, entonces v1 ≥ h.
Palabras Claves: Problema de Steklov, cono, curvatura media.
MSC2010: 35P15, 53C20, 53C42, 53C43
The Steklov problem on the cone
]]> Abstract. Let (Mn, g) be a cone of height 0 ≤ xn+1 ≤ 1 en ℝn+1, endowed with a rotationally invariant metric 2ds2 + ƒ2(s)dw2, where dw2 represents the standard metric on Sn-1, the (n - 1)-dimensional unit sphere. Assume Ric(g) ≥ 0. In this paper we prove that if h > 0 is the mean curvature on ∂M and v1 is the first eigenvalue of the Steklov problem, then v1 ≥ h.Texto Completo disponible en PDF
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*E-mail: oscar.montano@correounivalle.edu.co
Recibido: 13 de junio de 2012, Aceptado: 10 de septiembre de 2012.