36 citations · 94 across the 33 of their papers we have counts for
33 papers
On differential geometry of non-degenerate CR manifolds
Yuxin Dong, Yibin Ren
In this paper, we consider a non-degenerate CR manifold (M,H(M),J) with a given pseudo-Hermitian 1-form θ, and endow the CR distribution H(M) with any Hermitian metric h instead of…
Gradient Estimates For The CR Heat Equation On Complete noncompact Pseudo-Hermitian Manifolds
Yuxin Dong, Yibin Ren, Biqiang Zhao
In this paper, we derive local and global Li-Yau type gradient estimates for the positive solutions of the CR heat equation on complete noncompact pseudo-Hermitian manifolds. As ap…
On stability of subelliptic harmonic maps with potential
Tian Chong, Yuxin Dong, Guilin Yang
In this paper, we investigate the stability problem of subelliptic harmonic maps with potential. First, we derive the first and second variation formulas for subelliptic harmonic m…
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.
On subelliptic harmonic maps with potential
Yuxin Dong, Han Luo, Weike Yu
Let be a sub-Riemannian manifold and be a Riemannian manifold. For a smooth map , we consider the energy functional $E_G(u) = \frac{1}{2} \int_M[|…
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…