• Corpus ID: 229924216

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

  title={A Liouville theorem for M\"\{o\}bius invariant equations},
  author={Yanyan Li and Han-Chun Lu and Siyuan Lu},
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. 



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

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

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

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Some remarks on singular solutions of nonlinear elliptic equations. I

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

Boundary operators associated to the σ-curvature

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

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

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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