The Yang-Mills flow converges sharply on SU(r)-bundles over locally hyperKähler ALE 4-manifolds.
Integrable Deformations and Stability of the Ricci Flow
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We provide a comparatively simple proof of the dynamical stability of Ricci flow near a linearly stable Ricci-flat ALE metric with integrable deformations. Our proof relies on the equivalence between integrability and an "almost-orthogonality" property of the Ricci-DeTurck tensor, allowing us to analyze the latter directly. We obtain our main results in weighted Holder spaces and then show how to recover the $L^p$-stability theorems of Deruelle-Kroncke and Kroncke-Petersen.
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Convergence of the Yang-Mills flow on ALE gravitational instantons
The Yang-Mills flow converges sharply on SU(r)-bundles over locally hyperKähler ALE 4-manifolds.