Chang, Sun-Yung A.; Yang, Paul C. Fourth order equations in conformal geometry. (English) Zbl 0997.35016 Bourguignon, Jean Pierre (ed.) et al., Global analysis and harmonic analysis. Papers from the conference, Marseille-Luminy, France, May 1999. Paris: Société Mathématique de France. Sémin. Congr. 4, 155-165 (2000). Summary: The authors review some recent work on fourth-order equations in conformal geometry of three and four dimensions and discuss an existence result for a Yamabe-type equation in dimension three. Furthermore, they examine a generalization of the Cohn-Vossen inequality to dimension four and, finally, review an application of the fourth-order equation to a fully nonlinear equation in dimension four that involves the Ricci tensor.For the entire collection see [Zbl 0973.00041]. Cited in 7 Documents MSC: 35J60 Nonlinear elliptic equations 58E15 Variational problems concerning extremal problems in several variables; Yang-Mills functionals Keywords:Paneitz operator; Gauss-Bonnet formula; Yamabe-type equation; Cohn-Vossen inequality PDFBibTeX XMLCite \textit{S.-Y. A. Chang} and \textit{P. C. Yang}, Sémin. Congr. 4, 155--165 (2000; Zbl 0997.35016) Full Text: EMIS EMIS