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      Conjetura de Escobar para el primer valor propio de Steklov sobre n-elipsoides Translated title: Escobar’s Conjecture for the First Steklov Eigenvalue on n-ellipsoids

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          Abstract

          Resumen Sea M un elipsoide en ℝ n ; n ≥ 3, si la segunda forma fundamental π satisface π(υ,υ) ≥ k |ʋ|2 sobre ∂M, k > 0, entonces el primer valor propio de Steklov ν 1(M) satisface la desigualdad ν 1(M) ≥ k. La igualdad se obtiene si y sólo si M es la bola de radio 1/k. Este resultado verifica la conjetura de Escobar para n-elipsoides.

          Translated abstract

          Abstract 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.

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          Most cited references 7

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          Some Isoperimetric Inequalities for Harmonic Functions

           L. Payne (1970)
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            An Isoperimetric Inequality and the First Steklov Eigenvalue

             José Escobar (1999)
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              The Geometry of the First Non-zero Stekloff Eigenvalue

               José Escobar (1997)
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                Author and article information

                Contributors
                Role: ND
                Journal
                rcien
                Revista de Ciencias
                rev. cienc.
                Universidad del Valle (Cali, Valle, Colombia )
                0121-1935
                December 2016
                : 20
                : 2
                : 55-61
                Affiliations
                Cali Valle del Cauca orgnameUniversidad del Valle orgdiv1Departamento de Matemáticas Colombia oscar.montano@ 123456correounivalle.edu.co
                Article
                S0121-19352016000200055
                10.25100/rc.v20i2.4673

                This work is licensed under a Creative Commons Attribution 4.0 International License.

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                Figures: 0, Tables: 0, Equations: 0, References: 7, Pages: 7
                Product
                Product Information: SciELO Colombia

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