Conformal metrics on the four-dimensional half sphere with symmetric $Q$
and $T$ curvatures
Conformal metrics on the four-dimensional half sphere with symmetric $Q$
and $T$ curvatures
In this paper, we address the problem of prescribing non-constant $Q$ and boundary $T$ curvatures on the upper hemisphere $\mathbb{S}^4_+\subset \mathbb{R}^5$, via a conformal change of the background metric. This is equivalent to solve a fourth-order non-linear elliptic boundary value problem with a third-order non-linear equation and homogeneous Neumann conditions …