arXiv research

We give exposition of a Liouville theorem established in \cite{Li3} which is a novel extension of the classical Liouville theorem for harmonic functions. To illustrate some ideas of the proof of the Liouville theorem, we present a new proof of the classical Liouville theorem for harmonic functions. Applications of the …

Article proves Liouville theorem for heat equation in super Ricci flow.

The Liouville theorem is proven for V T-harmonic map heat flow.

Study explores Liouville's theorem and SLP for harmonic functions on cones and surfaces.

The paper classifies invariant operators and proves a Liouville theorem.

Study Liouville theorem for specific harmonic maps.

The paper investigates Liouville type theorems for various harmonic forms on Riemannian manifolds.

Optimal Liouville theorem for half-Euclidean space equations.

The paper proves three circles theorems and Liouville type theorems for subharmonic and holomorphic functions.

The paper derives Liouville theorems for various generalized maps on Riemannian manifolds.

Study Liouville theorems for harmonic maps along ancient super Ricci flows.

The paper proves a Liouville theorem for heat flows on manifolds with specific curvature conditions.

The paper proves a Liouville theorem for specific harmonic maps with free boundary.

Proves a Liouville-type theorem for p-Laplacian on manifolds.

Improved Liouville theorems for ancient solutions to V-harmonic map heat flows.

Study proves Liouville theorem for specific curvature equations with boundary conditions.

Paper proves a Liouville theorem for solitons with constant curvature.

Liouville theorems extended to graphs with bounded geometry.

Gradient bounds and Liouville theorems for quasi-linear equations on manifolds with nonnegative Ricci curvature.

The paper establishes gradient estimates and Liouville theorems for Φ-Laplacian equations on Riemannian manifolds.

The Liouville theorem is proven for harmonic maps from a specific type of manifold.

Paper proves a Liouville theorem for a generalized elliptic equation on H-type groups.

We study the Liouville type theorems for transversally harmonic and biharmonic maps on foliated Riemannian manifolds

We establish a general Liouville type theorem for conformally invariant fully nonlinear equations.

The paper extends Liouville theorems to sub-Riemannian manifolds.

The paper proves Liouville-type theorems on Hadamard manifolds.

Sharp Liouville theorem for minimal graphs on manifolds with nonnegative Ricci curvature.

Ancient Lagrangian flows get limited convex solutions.

The paper proves Liouville theorems for $V$-harmonic maps under specific curvature conditions.

We present some further results on Liouville type theorems for some conformally invariant fully nonlinear equations.

In the present paper we prove Liouville-type theorems: non-existence theorems for complete twisted and warped products of Riemannian manifolds which generalize and complement similar results for compact manifolds.

Local gradient estimates for eigenfunctions on conformal solitons improve Liouville theorems.

The paper proves Liouville theorems and nonexistence results for semilinear equations on pseudo-Hermitian manifolds.

L. Capogna and M. Cowling showed that if $φ$ is 1-quasiconformal on an open subset of a Carnot group G, then composition with $φ$ preserves Q-harmonic functions, where Q denotes the homogeneous dimension of G. Then they combine this with a regularity theorem for Q-harmonic functions to show that $φ$ is in fact $C^\inft…

The paper extends Liouville's theorem to calibrated geometries in various dimensions.

This paper proves Liouville theorems for conformally invariant fully nonlinear equations.

Study proves unique compactification of hyperbolic space.

The paper proves a hierarchy of Liouville theorems for polyharmonic functions on manifolds with nonnegative Ricci curvature.

For $n\geq2,$ we obtain Liouville type theorems for minimal surface equations in half space $\mathbf R^n_+$ with affine Dirichlet boundary value or constant Neumann boundary value.

We prove a Liouville theorem for the plurisubharmonic functions on complete Kaelher manifolds. As the applications, we prove a splitting theorem for complete Kaehler manifolds with nonnegative biscetional curvature in terms of the linear growth harmonic functions and a optomal gap theorem for such manifolds.

The paper extends a Liouville theorem to biharmonic functions on manifolds with nonnegative Ricci curvature.

In this short paper we study $L_f^p$-Liouville property with $0<p<1$ for nonnegative $f$-subharmonic functions on a complete noncompact smooth metric measure space $(M,g,e^{-f}dv)$ with $\mathrm{Ric}_f^m$ bounded below for $0<m\leq\infty$. We prove a sharp $L_f^p$-Liouville theorem when $0<m<\infty$. We also prove an $…

Paper proves flatness of anisotropic minimal graphs in half-spaces.

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 Kähler manifolds to the complete non-Kähler case.

In the present paper we prove Liouville-type theorems: non-existence theorems for some complete Riemannian almost product manifolds and special mappings of complete Riemannian manifolds which generalize similar results for compact manifolds.

Paper proves Liouville-type theorems for minimal graphs with capillary boundary.

Optimal Liouville theorem for minimal disks in any codimension.

Paper proves constant functions for pluriharmonic on certain solitons.