Liouville Type Theorems for Lichnerowicz Equations and Ginzburg-Landau Equation: Survey

Li Ma

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DOI: 10.4236/apm.2011.13022                

Abstract

In this survey paper, we firstly review some existence aspects of Lichnerowicz equation and Ginzburg-Landau equations. We then discuss the uniform bounds for both equations in Rn. In the last part of this report, we consider the Liouville type theorems for Lichnerowicz equation and Ginzburg-Landau equations in Rn via two approaches from the use of maximum principle and the monotonicity formula

Keywords

Liouville Theorems, Ancient Solution, Ginzburg-Landau Equation, Lichenrowicz Equation

Conflicts of Interest

The authors declare no conflicts of interest.

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