Existence and uniqueness of toric ALE and ALF Ricci-flat gravitational instantons for admissible rod structures, with toric self-dual instantons being multi-Eguchi-Hanson or multi-Taub-NUT.
Li,Classification results for conformally Kähler gravitational instantons, [arXiv:2310.13197 [math.DG]]
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Toric self-dual Einstein instantons with negative cosmological constant satisfying a global conformal Kähler extension condition are precisely the Calderbank-Pedersen-Singer multipole solutions.
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.
Einstein metrics extending Chen-Teo geometries with cosmological constant are either Plebański-Demiański or anti-self-dual Weyl cases, yielding for lambda<0 a conformal infinity between asymptotically hyperbolic ends, one conformal to an ALE scalar-flat Kähler metric, plus new instanton topologies a
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On the existence of toric ALE and ALF gravitational instantons
Existence and uniqueness of toric ALE and ALF Ricci-flat gravitational instantons for admissible rod structures, with toric self-dual instantons being multi-Eguchi-Hanson or multi-Taub-NUT.
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On toric self-dual Einstein gravitational instantons
Toric self-dual Einstein instantons with negative cosmological constant satisfying a global conformal Kähler extension condition are precisely the Calderbank-Pedersen-Singer multipole solutions.
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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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On Chen-Teo geometries with cosmological constant
Einstein metrics extending Chen-Teo geometries with cosmological constant are either Plebański-Demiański or anti-self-dual Weyl cases, yielding for lambda<0 a conformal infinity between asymptotically hyperbolic ends, one conformal to an ALE scalar-flat Kähler metric, plus new instanton topologies a