Perturbative techniques in conformal geometry

  • Andrea Malchiodi

    Scuola Normale Superiore, Pisa, Italy
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Abstract

This paper reviews some results, mostly perturbative in nature, concerning the prescription of scalar curvature via conformal deformation of the metric on a compact manifold. This problem consists in solving a nonlinear elliptic equation with critical power, leading to non-compactness phenomena. We will see how some finite-dimensional reduction of the problem in certain situations, jointly with the variational structure, can help in finding existence and multiplicity results.

Cite this article

Andrea Malchiodi, Perturbative techniques in conformal geometry. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 33 (2022), no. 3, pp. 507–533

DOI 10.4171/RLM/978