Calculus of Variations and Geometric Measure Theory

Prescribing Morse scalar curvatures in high dimension

Andrea Malchiodi (Scuola Normale Superiore)

created by pinamonti on 17 Mar 2021

23 mar 2021 -- 14:30   [open in google calendar]

Zoom seminar

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We consider the classical question of prescribing the scalar curvature of a manifold via conformal deformations of the metric, dating back to works by Kazdan and Warner. This problem is mainly understood in low dimensions, where blow-ups of solutions are proven to be "isolated simple". We find natural conditions to guarantee this also in arbitrary dimensions, when the prescribed curvatures are Morse functions. As a consequence, we improve some pinching conditions in the literature and derive existence and non-existence results of new type. This is joint work with M. Mayer.