FOURTH ORDER EQUATIONS IN CONFORMAL GEOMETRY by Sun - Yung
نویسندگان
چکیده
— In this article we review some recent work on fourth order equations in conformal geometry of three and four dimensions. We discuss an existence result for a Yamabe-type equation in dimension three. We examine a generalization of the Cohn-Vossen inequality to dimension four. Finally, we review an application of the fourth order equation to a fully nonlinear equation in dimension four that involves the Ricci tensor. Résumé (Équations d’ordre quatre en géométrie conforme). — Dans cet article, nous présentons un travail récent sur des équations d’ordre quatre en géométrie conforme de dimensions trois et quatre. On présente un résultat d’existence d’une équation de type Yamabe en dimension trois. On examine une généralisation de l’inégalité de Cohn-Vossen en dimension quatre. Finalement, nous donnons une application, en dimension quatre, de l’équation d’ordre quatre à une équation non linéaire faisant intervenir le tenseur de Ricci.
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