Curvature flows on four manifolds with boundary

Details Curvature flows on four manifolds with boundary Curvature flows on four manifolds with boundary

2007-08-15

arxiv.org/abs/0708.2029v1

Mathematics

Analysis of PDEs

Scientific paper

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 and the evolution equation by $T$-curvature at the boundary with the condition that the $Q$-curvature and the mean curvature vanish. Using integral method, we prove global existence and convergence for the $Q$-curvature flow (resp $T$-curvature flow) to smooth metric of prescribed $Q$-curvature (resp $T$-curvature) under conformally invariant assumptions.

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