Abstract

MONTANO CARRENO, ÓSCAR ANDRÉS. The Stekloff Problem for Rotationally Invariant Metrics on the Ball. Rev.colomb.mat. [online]. 2013, vol.47, n.2, pp.181-190. ISSN 0034-7426.

Let (B_r,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 S^n-1, the (n-1)--dimensional unit sphere. Assume that B_r has non--negative sectional curvature. In this paper we prove that if h(r)>0 is the mean curvature on ∂ B_r 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.

Keywords : Stekloff eigenvalue; Rotationally invariant metric; Non-negative sectional curvature.

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