2022/06/22 by Chen, Hang, Gui, Xudong · 1 citation
#53C42 (Primary) 35P15 (Secondary) #58C40 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2206.11164
Let M be an m (≥2)-dimensional closed orientable submanifold in an n-dimensional complete simply-connected Riemannian manifold N, where the sectional curvature of N is bounded above by δ. When δ<0, inspired by Niu-Xu (arXiv:2106.01912), we give new upper bounds for the first nonzero eigenvalues of the p-Laplacian and the LT operator, respectively. These generalize Niu-Xu's work for the Laplacian (arXiv:2106.01912) and improve the estimates due to Chen (Nonlinear Anal.,196, 111833, 2020) for the p-Laplacian and Grosjean (Hokkaido Math. J., 33(2) , 319-339, 2004) for the LT operator, respectively. We also obtain several Reilly-type inequalities for the weighted manifolds and some boundary value problems.