Tiến Sĩ Existence of conformal metrics with constant Qcurvature

Abstract
Given a compact four dimensional manifold, we prove existence of conformal metrics with constant Q-curvature under generic assumptions. The
problem amounts to solving a fourth-order nonlinear elliptic equation with
variational structure. Since the corresponding Euler functional is in general
unbounded from above and from below, we employ topological methods and
min-max schemes, jointly with the compactness result of [35].