A Pisan workshop in geometric analysis

Existence and asymptotic behavior of non-normal conformal metrics on R⁴ with sign-changing Q-curvature

speaker: Chiara Bernardini (Università degli Studi di Padova)

abstract: We study a prescribed Q-curvature problem in the Euclidean space R^4, assuming to have power-type and sign-changing Q-curvature. Geometrically, finding a solution to this problem, corresponds to find a metric conformal to the Euclidean one on R^4, which has the assigned prescribed Q-curvature. First, under suitable assumptions, we prove existence of non-normal solutions to our problem, extending in this way some previous results. Then, we prove a classification result, which allows us to characterize solutions in terms of the behavior at infinity of the scalar curvature of the associated conformal metric. We also present the corresponding problem on the plane.

timetable:
Wed 20 Sep, 15:30 - 16:30, Aula Dini
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