Reilly-type inequalities for p-Laplacian on submanifolds in space forms. (July 2019) - Chen, Hang; Wei, Guofang
Abstract: Let M be an n -dimensional closed orientable submanifold in an N -dimensional space form. When 1 < p ≤ n 2 + 1, we obtain an upper bound for the first nonzero eigenvalue of the p -Laplacian in terms of the mean curvature of M and the curvature of the space form. This generalizes the Reilly inequality for the Laplacian (Soufi and Ilias, 1992; Reilly, 1977) to the p -Laplacian and extends the work of Du and Mao (2015) for the p -Laplacian.