The mass of toric ALE or ALF 4-manifolds with nonnegative scalar curvature is at least the mass of the corresponding toric gravitational instanton plus a term from its conical defects, with equality only when the manifold is Ricci-flat and identical to that instanton.
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Existence and uniqueness theorems for complete noncompact G2-holonomy metrics with ALC asymptotics, including a G2-analogue of the Atiyah-Hitchin metric, plus moduli theory and rigidity results via a general Fredholm theory on ALC manifolds.
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A Comparison Theorem For the Mass of ALE and ALF Toric 4-Manifolds
The mass of toric ALE or ALF 4-manifolds with nonnegative scalar curvature is at least the mass of the corresponding toric gravitational instanton plus a term from its conical defects, with equality only when the manifold is Ricci-flat and identical to that instanton.
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Complete noncompact G2-manifolds with ALC asymptotics
Existence and uniqueness theorems for complete noncompact G2-holonomy metrics with ALC asymptotics, including a G2-analogue of the Atiyah-Hitchin metric, plus moduli theory and rigidity results via a general Fredholm theory on ALC manifolds.