Abstract
Given a compact four-dimensional smooth Riemannian manifold (M,g) with smooth boundary, we consider the evolution equation by Q-curvature in the interior keeping the T-curvature and the mean curvature to be zero. Using integral methods, we prove global existence and convergence for the Q-curvature flow to a smooth metric conformal to g of prescribed Q-curvature, zero T-curvature and vanishing mean curvature under conformally invariant assumptions.
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Ndiaye, C.B. Q-curvature flow on 4-manifolds with boundary. Math. Z. 269, 83–114 (2011). https://doi.org/10.1007/s00209-010-0717-2
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DOI: https://doi.org/10.1007/s00209-010-0717-2