Related papers: Liouville properties of plurisubharmonic functions
In this paper, we study global properties of continuous plurisubharmonic functions on complete noncompact K\"ahler manifolds with nonnegative bisectional curvature and their applications to the structure of such manifolds. We prove that…
We prove a linear trace Li-Yau-Hamilton inequality for the Kaehler-Ricci flow. We then use this sharp differential inequality to study the Liouville properties of the plurisubharmonic functions on complete Kaehler manifolds with nonnegative…
In this paper we prove a gap theorem for K\"ahler manifolds with nonnegative orthogonal bisectional curvature and nonnegative Ricci curvature, which generalizes an earlier result of the first author. We also prove a Liouville theorem for…
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…
We derive some consequences of the Liouville theorem for plurisubharmonic functions of L.-F. Tam and the author. The first result provides a nonlinear version of the complex splitting theorem (which splits off a factor of $\mathbb{C}$…
We review and give elementary proofs of Liouville type properties of harmonic and subharmonic functions in the plane endowed with a complete Riemannian metric, and prove a gap theorem for the possible growth of harmonic functions when this…
In this paper, we prove a Liouville theorem for holomorphic functions on a class of complete Gauduchon manifolds. This generalizes a result of Yau for complete K\"ahler manifolds to the complete non-K\"ahler case.
In this article, we prove a Liouville property of holomorphic maps from a complete Kahler manifold with nonnegative holomorphic bisectional curvature to a complete simply connected Kahler manifold with a certain assumption on the sectional…
In this paper, we establish a complete Liouville--type hierarchy for polyharmonic functions on Riemannian manifolds with nonnegative Ricci curvature. Extending Yau's classical result for harmonic functions and our recent biharmonic…
We explore Liouville's theorem and the Strong Liouville Property (SLP) for harmonic functions on Riemannian cones and surfaces. Our approach recasts the classical Liouville property in terms of the growth of radial eigenfunctions (in the…
In this paper, we will use the normalized intetral Ricci curvature to investigate Liouville type property of $ p $ harmonic function on Riemannian manifold. secondly, we will use the BiRic curvature to obtian Liuville theorem for $ p $…
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.…
We study the Liouville type theorems for transversally harmonic and biharmonic maps on foliated Riemannian manifolds
We introduce and study an approximate solution of the p-Laplace equation, and a linearlization $L_{\epsilon}$ of a perturbed p-Laplace operator. By deriving an $L_{\epsilon}$-type Bochner's formula and a Kato type inequality, we prove a…
In this paper, we prove some splitting results for manifolds supporting a non-constant infinity harmonic function which has at most linear growth on one side. Manifolds with non-negative Ricci or sectional curvature are considered. In…
This paper is a study of harmonic maps from Riemannian polyhedra to (locally) non-positively curved geodesic spaces in the sense of Alexandrov. We prove Liouville-type theorems for subharmonic functions and harmonic maps under two different…
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…
We prove a Liouville property for any $f$-harmonic function with polynomial growth on a complete noncompact smooth metric measure space $(M,g,e^{-f}dv)$ when the Bakry-\'Emery Ricci curvature is nonnegative and its diameter of geodesic…
We prove a Liouville type theorem for entire maximal $m$-subharmonic functions in $\mathbb C^n$ with bounded gradient. This result, coupled with a standard blow-up argument, yields a (non-explicit) a priori gradient estimate for the complex…
We present a new, short and independent proof of the Liouville-type theorem for entire and subharmonic functions of finite order bounded outside some set of zero planar density.