Revista Integración
ISSN 0120-419X
MONTANO, ÓSCAR ANDRéS. The Steklov problem on the cone. []. , 30, 2, pp.121-128. ISSN 0120-419X.
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.
: Steklov problem; cone; mean curvature.