2 citations · 5 across the 10 of their papers we have counts for
11 papers
Spectral Bernstein theorems for submanifolds in Euclidean spaces
Yuxin Dong, Hezi Lin, Wei Zhang
In this paper, we consider the essential spectrum of submanifolds in Euclidean spaces under various geometric hypotheses. Our results involve extrinsic conditions such as finite to…
Gradient estimates for -harmonic functions on Riemannian manifolds
Yuxin Dong, Hezi Lin, Weihao Zheng
In this paper, we study -harmonic functions on complete Riemannian manifolds using the Moser iteration method. A volume comparison theorem and a Sobolev embedding theorem ar…
Hardy type inequalities on manifolds with nonnegative Ricci curvature
Yuxin Dong, Hezi Lin, Lingen Lu
We prove the Heisenberg-Pauli-Weyl inequality, Hardy-Sobolev inequality, and Caffarelli-Kohn-Nirenberg (CKN) inequality on manifolds with nonnegative Ricci curvature and Euclidean…
Sobolev Inequality on Manifolds With Asymptotically Nonnegative Bakry-Émery Ricci Curvature
Yuxin Dong, Hezi Lin, Lingen Lu
In this paper, inspired by [4, 9], we prove a Sobolev inequality on manifolds with density and asymptotically nonnegative Bakry-Émery Ricci curvature.
Sobolev Inequalities In Manifolds With Asymptotically Nonnegative Curvature
Yuxin Dong, Hezi Lin, Lingen Lu
Using the ABP-method as in a recent work by Brendle, we establish some sharp Sobolev and isoperimetric inequalities for compact domains and submanifolds in a complete Riemannian ma…
Gradient estimate and Liouville theorems for p-harmonic maps
Yuxin Dong, Hezi Lin
In this paper, we first obtain an gradient estimate for -harmonic maps, by assuming the target manifold supporting a certain function, whose gradient and Hessian satisfy s…
curvature pinching theorems and vanishing theorems on complete Riemannian manifolds
Yuxin Dong, Hezi Lin, Shihshu Walter Wei
In this paper, by using monotonicity formulas for vector bundle-valued -forms satisfying the conservation law, we first obtain general global rigidity theorems for locally…
Rigidity theorems of complete Kähler-Einstein manifolds and complex space forms
Tian Chong, Yuxin Dong, Hezi Lin +1
We derive some elliptic differential inequalities from the Weitzenböck formulas for the traceless Ricci tensor of a Kähler manifold with constant scalar curvature and the Bochner t…
Rigidity Theorems for Complete Sasakian Manifolds with Constant Pseudo-Hermitian Scalar Curvature
Yuxin Dong, Hezi Lin, Yibin Ren
The orthogonal decomposition of the Webster curvature provides us a way to characterize some canonical metrics on a pseudo-Hermitian manifold. We derive some subelliptic differenti…
Monotonicity formulae, vanishing theorems and some geometric applications
Yuxin Dong, Hezi Lin
Using the stress energy tensor, we establish some monotonicity formulae for vector bundle-valued p-forms satisfying the conservation law, provided that the base Riemannian (resp. K…
Liouville theorems for F-harmonic maps and their applications
Yuxin Dong, Hezi Lin, Guilin Yang
We prove several Liouville theorems for F-harmonic maps from some complete Riemannian manifolds by assuming some conditions on the Hessian of the distance function, the degrees of…