4 papers · 1 filter
Refined Kato type inequalities and new vanishing theorems on complete Kähler and quaternionic Kähler manifolds
Dinh Tien Dat, Nguyen Thac Dung, Yong Luo
Given a complete Riemannian manifold satisfying a weighted Poincaré inequality and having a bounded below Ricci curvature, various vanishing theorems for harmonic functions and har…
Gap theorems for complete submanifolds in the hyperbolic space
Jianling Liu, Yong Luo
Based on the seminal Simons' formula, Shen \cite{Shen} and Lin-Xia \cite{LX} obtained gap theorems for compact minimal submanifolds in the unit sphere in the late 1980's. Then due…
Universal inequalities for eigenvalues of the Dirichlet Laplacian on conformally flat Riemannian manifolds
Yong Luo, Xianjing Zheng
In this paper we study eigenvalues of the Dirichlet Laplacian on conformally flat Riemannian manifolds. In particular we establish some universal inequality for eigenvalues of the…
Inequalities for eigenvalues of Laplacian and biharmonic operators on submanifolds
Yong Luo, Xianjing Zheng
In this paper we study eigenvalues of Laplacian and biharmonic operators on compact domains in complete manifolds. We establish several new inequalities for eigenvalues of Laplacia…