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El problema de Steklov sobre el cono

Keywords: steklov problem, cone, mean curvature.

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Abstract:

let (mn, g) be a cone of height 0 ≤ xn+1 ≤ 1 en ?n+1, endowed with a rotationally invariant metric 2ds2 + ?2(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.

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