相关论文: CR Sub-Laplacian Comparison and Liouville-type The…

This paper mainly focuses on the CR analogue of the three-circle theorem in a complete noncompact pseudohermitian manifold of vanishing torsion being odd dimensional counterpart of K\"ahler geometry. In this paper, we show that the CR…

In this paper, we derive a sub-gradient estimate for pseudoharmonic maps from noncompact complete Sasakian manifolds which satisfy CR sub-Laplace comparison property, to simply-connected Riemannian manifolds with nonpositive sectional…

This is the very first paper to focus on the CR analogue of Yau's uniformization conjecture in a complete noncompact pseudohermitian $(2n+1)$-manifold of vanishing torsion (i.e. Sasakian manifold) which is an odd dimensional counterpart of…

In this paper, we will give a horizontal gradient estimate of positive solutions of $\Delta_b u = - \lambda u$ on complete noncompact pseudo-Hermitian manifolds. As a consequence, we recapture the Liouville theorem of positive…

In this paper, we give an estimate of sub-Laplacian of Riemannian distance functions in pseudo-Hermitian geometry which plays a similar role as Laplacian comparison theorem in Riemannian geometry, and deduce a prior horizontal gradient…

In this paper, we study the CR Yamabe type equation \begin{align} \Delta_b u+F(u)=0 \nonumber \end{align} on complete noncompact $(2n+1)$-dimensional Sasakian manifolds with nonnegative curvature. Under some assumptions, we prove a rigidity…

This work deals with the Entire solutions of a nonlinear equation. The first part of this paper is devoted to investigation of the Liouville property on compact manifolds, which extends a result by Castorina-Mantegazza [4] for positive f.…

A Liouville-type result for the p-Laplacian on complete Riemannian manifolds is proved. As an application are present some results concerning complete non-compact hypersurfaces immersed in a suitable warped product manifold.

We establish a new version of the CR almost Schur Lemma which gives an estimation of the pseudohermitian scalar curvature on a compact strictly pseudoconvex pseudohermitian manifold to be a constant in terms of the norm of the traceless…

In this paper, we derive the gradient estimates for the positive solutions of the equation $\Delta_b u + au^{p+1} = 0$ on complete noncompact pseudo-Hermitian manifolds, where $a > 0$ and $p \leq 0$ or $a < 0$ and $p > 0$ are two constants.…

In this paper, by applying a linear trace Li-Yau-Hamilton inequality for a positive (1,1)-form solution of the CR Hodge-Laplace heat equation and monotonicity of the heat equation deformation, we obtain an optimal gap theorem for a complete…

In this paper, we discuss the validity of the Liouville property for $X$-harmonic functions, i.e. positive solution to $\Delta_{X}u=0$, where $X$ is a vector field on a complete, non-compact Riemannian manifold and $\Delta_{X}$ is the…

In this paper, we solve the so-called CR Poincar\'e-Lelong equation by solving the CR Poisson equation on a complete noncompact CR $(2n+1)$-manifold with nonegative pseudohermitian bisectional curvature tensors and vanishing torsion which…

In this note we will provide a gradient estimate for harmonic maps from a complete noncompact Riemannian manifold with compact boundary (which we call "Kasue manifold") into a simply connected complete Riemannian manifold with non-positive…

In this paper, we show that there exists a nonconstant CR holomorphic function of polynomial growth in a complete noncompact Sasakian manifold of nonnegative pseudohermitian bisectional curvature with the CR maximal volume growth property.…

In this paper we study positive solutions to the CR Yamabe equation in noncompact $(2n+1)$-dimensional Sasakian manifolds with nonnegative curvature. In particular, we show that the Heisenberg group $\mathbb{H}^1$ is the only (complete)…

In this paper, we concern with the Sasaki analogue of Yau uniformization conjecture in a complete noncompact Sasakian manifold with nonnegative transverse bisectional curvature. As a consequence, we confirm that any $5$-dimensional complete…

In this paper we extend Yau's celebrated Liouville theorem to the biharmonic case. Namely, we show that in a complete Riemannian manifold with a pole and nonnegative Ricci curvature, any biharmonic function of subquadratic growth must be…

Let $(M,J,\theta)$ be a complete pseudo-Hermitian manifold which satisfies the CR sub-Laplacian comparison property. In this paper, we derive the local subgradient estimates for positive solutions to the following nonlinear subparabolic…

We prove the equivalence of several natural notions of conformal maps between sub-Riemannian manifolds. Our main contribution is in the setting of those manifolds that support a suitable regularity theory for subelliptic $p$-Laplacian…