Abstract

MONTANO, ÓSCAR ANDRéS. The Steklov problem on the cone. Integración - UIS [online]. 2012, vol.30, n.2, pp.121-128. ISSN 0120-419X.

Let (Mⁿ, g) be a cone of height 0 ≤ x_n+1 ≤ 1 en ℝⁿ⁺¹, endowed with a rotationally invariant metric 2ds² + ƒ²(s)dw², where dw² represents the standard metric on S^n-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.

Keywords : Steklov problem; cone; mean curvature.

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