The Stekloff Problem for Rotationally Invariant Metrics on the Ball
Let (Br,g) be a ball of radius r>0 in Rn (n≥ 2) endowed with a rotationally invariant metric ds²+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 if h(r)>0 is the mean curvature on ∂ Br and ν1 is the first eigenvalue of the Stekloff problem, then ν1 ≥ h(r). Equality \big(ν 1 = h(r)\big) holds only for the standard metric of Rn.
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| Format: | Digital revista |
| Language: | English |
| Published: |
Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas
2013
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| Online Access: | http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262013000200005 |
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