In this Note, we prove the Liouville type result for smooth positive solutions to the Lichnerowicz equation in . 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.
Dans cette Note on démontre un résultat de type de Liouville des solutions régulières pour l'équation de Lichnerowicz dans . En utilisant la même méthode on détermine également une borne uniforme inférieure des solutions régulières pour l'équation de Ginzburg–Landau dans tout l'espace. Des résultats analogues sont donnés dans le cas d'une variété riemannienne non compacte complète de courbure de Ricci bornée inférieurement.
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Published online:
Li Ma 1
@article{CRMATH_2010__348_17-18_993_0, author = {Li Ma}, title = {Liouville type theorem and uniform bound for the {Lichnerowicz} equation and the {Ginzburg{\textendash}Landau} equation}, journal = {Comptes Rendus. Math\'ematique}, pages = {993--996}, publisher = {Elsevier}, volume = {348}, number = {17-18}, year = {2010}, doi = {10.1016/j.crma.2010.07.031}, language = {en}, }
TY - JOUR AU - Li Ma TI - Liouville type theorem and uniform bound for the Lichnerowicz equation and the Ginzburg–Landau equation JO - Comptes Rendus. Mathématique PY - 2010 SP - 993 EP - 996 VL - 348 IS - 17-18 PB - Elsevier DO - 10.1016/j.crma.2010.07.031 LA - en ID - CRMATH_2010__348_17-18_993_0 ER -
Li Ma. Liouville type theorem and uniform bound for the Lichnerowicz equation and the Ginzburg–Landau equation. Comptes Rendus. Mathématique, Volume 348 (2010) no. 17-18, pp. 993-996. doi : 10.1016/j.crma.2010.07.031. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.07.031/
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☆ The research is partially supported by the National Natural Science Foundation of China 10631020 and SRFDP 20090002110019.
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