Abstract

MONTANO CARRENO, ÓSCAR ANDRÉS. Upper bound for the first eigenvalue of the Steklov problem. Integración - UIS [online]. 2013, vol.31, n.1, pp.53-58. ISSN 0120-419X.

Let Br be an n-dimensional ball endowed with a rotationally in- variant metric and with non-positive radial sectional curvatures. If v is the first Steklov eigenvalue and h is the mean curvature on the boundary of the ball, we prove that v ≤ h. Equality holds only when B_r is the ball endowed with the standard metric of ℝⁿ.

Keywords : Sectional curvature; mean curvature; Steklov eigenvalue.

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