相关论文: Collapsing of $ALH^*$-Gravitational Instantons

In this letter we demonstrate that the intersection form of the Hausel--Hunsicker--Mazzeo compactification of a four dimensional ALF gravitational instanton is definite and diagonalizable over the integers if one of the Kahler forms of the…

We give a short proof of the Torelli theorem for $ALH^*$ gravitational instantons, using the authors' previous construction of mirror special Lagrangian fibrations in del Pezzo surfaces and rational elliptic surfaces together with recent…

We survey the authors recent works, joint with A. Jacob, on Strominger-Yau-Zaslow mirror symmetry for rational elliptic surfaces and del Pezzo surfaces. We discuss some applications, including the Torelli theorem for $ALH^*$ gravitational…

In this paper, we construct families of gravitational instantons of type ALG, ALG*, ALH and ALH* using a gluing construction. Away from a finite set of exceptional points, the metric collapses with bounded curvature to a quotient of…

We construct large families of new collapsing hyperk\"ahler metrics on the K3 surface. The limit space is the quotient of a flat 3-torus by an involution. Away from finitely many exceptional points the collapse occurs with bounded…

We prove that Hitchin's generalized Kaehler structure on the moduli space of instantons over a compact, even generalized Kaehler four-manifold may be obtained by generalized Kaehler reduction, in analogy with the usual Kaehler case. The…

We investigate the asymptotic geometry of Hermitian non-K\"ahler Ricci-flat metrics with finite $\int|Rm|^2$ at infinity. Specifically, we prove: 1. Any such metric is asymptotic to an ALE, ALF-A, AF, skewed special Kasner, ALH* model at…

We give an original analytic construction of hyperkahler ALF metrics on some ALE spaces of dihedral type, namely the spaces corresponding to minimal resolutions of Kleinian quotients relative to some binary dihedral group.

We construct the explicit form of three almost complex structures that a Riemannian manifold with self-dual curvature admits and show that their Nijenhuis tensors vanish so that they are integrable. This proves that gravitational instantons…

Physical properties of gravitational instantons which are derivable from minimal surfaces in 3-dimensional Euclidean space are examined using the Newman-Penrose formalism for Euclidean signature. The gravitational instanton that corresponds…

We study the space of square-integrable harmonic forms over ALF gravitational instantons of type $A _{ K -1 } $ and of type $D _K $. We first calculate its dimension making use of a result by Hausel, Hunsicker and Mazzeo which relates the…

Based on the uniformization theorems of gravitation instantons by Chen--Chen arXiv:1505.01790, Chen--Viaclovsky arXiv:2110.06498, Collins--Jacob--Lin arXiv:2111.09260, and Hein--Sun--Viaclovsky--Zhang arXiv:2111.09287, we prove that the…

This is our third paper in a series on the gravitational instantons. In this paper, we classify ALG and ALH gravitational instantons. In ALG case, we extend Hein's construction slightly and show that it's the only ALG gravitational…

In this paper, we will establish elliptic regularity estimates on families of gravitational instantons whose model metric near infinity collapse to a flat 3 dimensional space. We show that the constants in these estimates can be chosen…

We give a simple and uniform construction of essentially all known deformation classes of gravitational instantons with ALF, ALG or ALH asymptotics and nonzero injectivity radius. We also construct new ALH Ricci flat metrics asymptotic to…

We Study instanton solutions in general relativity with a scalar field. The metric ansatz we use is composed of a particular warp product of general Einstein metrics, such as those found in a number of cosmological settings, including…

We prove that the Gromov-Hausdorff compactification of the moduli space of Kahler-Einstein Del Pezzo surfaces in each degree agrees with certain algebro-geometric compactification. In particular, this recovers Tian's theorem on the…

It has long been conjectured that the Euclidean Schwarzschild and Euclidean Kerr instantons are the only non-trivial asymptotically flat (AF) gravitational instantons. In this letter, we show that this conjecture is false by explicitly…

There are two known classes of gravitational instantons with quadratic volume growth at infinity, known as type ALG and ALG$^*$. Gravitational instantons of type ALG were previously classified by Chen-Chen. In this paper, we prove a…

Yang-Mills instantons on ALE gravitational instantons were constructed by Kronheimer and Nakajima in terms of matrices satisfying algebraic equations. These were conveniently organized into a quiver. We construct generic Yang-Mills…