Extrinsic upper bound of the eigenvalue for p-Laplacian. (July 2020) - Chen, Hang
Abstract: Let M be an m -dimensional closed orientable submanifold in an n -dimensional Riemannian manifold N . When the sectional curvature of N is bounded above by δ, we obtain an upper bound for the first nonzero eigenvalue of the p -Laplacian in terms of the second fundamental form of M and δ . This generalizes the Reilly-type inequality for the Laplacian (Heintze, 1988; Reilly, 1977) to the p -Laplacian and extends the work of Chen and Wei (2019) and Du and Mao (2015) for the p -Laplacian.