Let M be a compact submanifold with boundary of a Euclidean space or a Sphere. In this paper, we derive an upper bound for the first non-zero eigenvalue p1 of Steklov problem on M in terms of the r-th mean curvatures of its boundary ∂ M. The upper bound obtained is sharp. © 2011 Elsevier B.V.
Ilias, S., & Makhoul, O. (2011). A Reilly inequality for the first Steklov eigenvalue. Differential Geometry and Its Application, 29(5), 699–708. https://doi.org/10.1016/j.difgeo.2011.07.005