The mass of any toric ALE/ALF 4-manifold with nonnegative scalar curvature is at least the mass of its corresponding toric gravitational instanton, corrected by conical angle defects, and equality holds only for the instanton.
A lojasiewicz inequality for ALE metrics.arXiv e-prints: 2007.09937
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Simplified proof of dynamical stability for Ricci flow near integrable linearly stable Ricci-flat ALE metrics via almost-orthogonality of the Ricci-DeTurck tensor.
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A Comparison Theorem For the Mass of ALE and ALF Toric 4-Manifolds
The mass of any toric ALE/ALF 4-manifold with nonnegative scalar curvature is at least the mass of its corresponding toric gravitational instanton, corrected by conical angle defects, and equality holds only for the instanton.
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Integrable Deformations and Stability of the Ricci Flow
Simplified proof of dynamical stability for Ricci flow near integrable linearly stable Ricci-flat ALE metrics via almost-orthogonality of the Ricci-DeTurck tensor.