3 papers
math.DG2026
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…
math.DG2025
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…
math.DG2024
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…