Liouville type theorem and uniform bound for the Lichnerowicz equation and the Ginzburg-Landau equation [Un théorème de type de Liouville et borne inférieure des solutions régulières pour l'équation de Lichnerowicz et pour l'équation de Ginsburg-Landau]

摘要

In this Note, we prove the Liouville type result for smooth positive solutions to the Lichnerowicz equation in R~n. Using the same method, we also give the uniform bound of the smooth solutions to Ginzburg-Landau equation in the whole space. Similar results on a complete non-compact Riemannian manifold with the Ricci curvature bounded from below are also considered.