The stekloff problem for rotationally invariant metrics on the ball
Let (Br,g) be a ball of radius r and gt;0 in Rn (n≥ 2) endowed with a rotationally invariant metricds2+f2(s)dw2, where dw2 represents the standard metric on Sn-1, the (n-1)--dimensional unit sphere. Assume that Br has non--negative sectional curvature. In this paper we prove that ifh(r) and gt;0 is...
- Autores:
-
Montaño Carreño, Óscar Andrés
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2013
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/49342
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/49342
http://bdigital.unal.edu.co/42799/
- Palabra clave:
- Valor propio de Stekloff
métrica rotacionalmente invariante
curvatura seccional no negativa
35P15
53C20
53C42
53C43
Stekloff eigenvalue
Rotationally invariant metric
Non-negative sectional curvature
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | Let (Br,g) be a ball of radius r and gt;0 in Rn (n≥ 2) endowed with a rotationally invariant metricds2+f2(s)dw2, where dw2 represents the standard metric on Sn-1, the (n-1)--dimensional unit sphere. Assume that Br has non--negative sectional curvature. In this paper we prove that ifh(r) and gt;0 is the mean curvature on ∂ Br and ν1 is the first eigenvalue of the Stekloff problem, thenν1 ≥ h(r). Equality (ν 1 = h(r)) holds only for the standard metric of Rn. |
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