4 papers · 1 filter
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…
Sobolev Inequality on Manifolds With Asymptotically Nonnegative Bakry-Ãmery 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-Ãmery Ricci curvature.
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…