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arxiv: 1505.01790 · v2 · pith:WW4GT6JB · submitted 2015-05-07 · math.DG · math-ph· math.MP

Gravitational instantons with faster than quadratic curvature decay (I)

Gao Chen , Xiuxiong Chen This is my paper

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classification math.DG math-phmath.MP
keywords gravitationalmustcasescurvaturedecayfasterinstantonsquadratic
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In this paper, we study gravitational instantons (i.e., complete hyperk\"aler 4-manifolds with faster than quadratic curvature decay). We prove three main theorems: 1.Any gravitational instanton must have known end----ALE, ALF, ALG or ALH. 2.In ALG and ALH-non-splitting cases, it must be biholomorphic to a compact complex elliptic surface minus a divisor. Thus, we confirm a long-standing question of Yau in ALG and ALH cases. 3.In ALF-D_k case, it must have an O(4)-multiplet.

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  1. On toric self-dual Einstein gravitational instantons

    math.DG 2026-06 unverdicted novelty 7.0

    Toric self-dual Einstein instantons with negative cosmological constant satisfying a global conformal Kähler extension condition are precisely the Calderbank-Pedersen-Singer multipole solutions.