| Abstract: |
| In this talk, we will consider the question of compactness for the higher-order Yamabe equation. This amounts to studying compactness (in $C^2k$) of nonnegative solutions of a $2k$-th order critical exponent elliptic equation, involving the GJMS operator, on a closed Riemannian manifold of dimension $\ge 2k+1$. Here $k$ is a positive integer. We will assume positivity conditions on the GJMS operator and establish uniform bounds on the (geometric) solutions under appropriate geometric assumptions. This is a joint project with Bruno Premoselli (ULB Brussels). |
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