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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].

MSC:

35J60 Nonlinear elliptic equations
58E15 Variational problems concerning extremal problems in several variables; Yang-Mills functionals
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