Abstract

MONTANO CARRENO, Óscar Andrés. Escobar’s Conjecture for the First Steklov Eigenvalue on n-ellipsoids. rev. cienc. [online]. 2016, vol.20, n.2, pp.55-61. ISSN 0121-1935.  https://doi.org/10.25100/rc.v20i2.4673.

Let M an ellipsoid in ℝ n , n ≥ 3, if the second fundamental form π satisfies π(υ,υ) ≥ k |ʋ|2 on ∂M, k > 0, then the first Steklov eigenvalue ν 1(M) satisfies the inequality ν 1(M) ≥ k. Equality is obtained only if M is the ball of radius 1/k. This result verifies Escobar’s conjecture for n- ellipsoids.

Keywords : Steklov eigenvalue; ellipsoid; second fundamental form.

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