• Corpus ID: 229924216

# A Liouville theorem for M\"{o}bius invariant equations

@inproceedings{Li2020ALT,
title={A Liouville theorem for M\"\{o\}bius invariant equations},
author={Yanyan Li and Han-Chun Lu and Siyuan Lu},
year={2020}
}
• Published 31 December 2020
• Mathematics
In this paper we classify Möbius invariant differential operators of second order in two dimensional Euclidean space, and establish a Liouville type theorem for general Möbius invariant elliptic equations.

## References

SHOWING 1-10 OF 47 REFERENCES

### An equation of Monge-Ampère type in conformal geometry, and four-manifolds of positive Ricci curvature

• Mathematics
• 2002
We formulate natural conformally invariant conditions on a 4-manifold for the existence of a metric whose Schouten tensor satisfies a quadratic inequality. This inequality implies that the

### Comparison Principles for Some Fully Nonlinear Sub-Elliptic Equations on the Heisenberg Group

• Mathematics
Analysis in Theory and Applications
• 2019
In this paper, we prove a form of the strong comparison principle for a class of fully nonlinear subelliptic operators of the form $\nabla^{2}_{H}\psi+L(\cdot,\psi,\nabla_{H}\psi)$ on the Heisenberg

### Some remarks on singular solutions of nonlinear elliptic equations. I

• Mathematics
• 2009
Abstract.We study strong maximum principles for singular solutions of nonlinear elliptic and degenerate elliptic equations of second order. An application is given on symmetry of positive solutions

### Complete Conformal Metrics of Negative Ricci Curvature on Euclidean Spaces

We show the existence and nonexistence results of complete conformal metrics with prescribed symmetric functions of the eigenvalues of the Ricci tensor defined on negative cones on Euclidean spaces.

### Min‐Oo Conjecture for Fully Nonlinear Conformally Invariant Equations

• Mathematics
Communications on Pure and Applied Mathematics
• 2019
In this paper we show rigidity results for supersolutions to fully nonlinear, elliptic, conformally invariant equations on subdomains of the standard n‐sphere Sn under suitable conditions along the

### Escobar type theorems for elliptic fully nonlinear degenerate equations

• Mathematics
American Journal of Mathematics
• 2019
abstract:In this paper we prove non-existence and classification results for elliptic fully nonlinear elliptic degenerate conformal equations on certain subdomains of the sphere with prescribed

### Degree theory for second order nonlinear elliptic operators and its applications

We introduce, along the lines of [4], an integer valued degree for second order fully nonlinear elliptic operators which is invariant under homotopy within elliptic operators. We also give some