TITLE:
Liouville Type Theorems for Lichnerowicz Equations and Ginzburg-Landau Equation: Survey
AUTHORS:
Li Ma
KEYWORDS:
Liouville Theorems, Ancient Solution, Ginzburg-Landau Equation, Lichenrowicz Equation
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.1 No.3,
June
3,
2011
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