相关论文: The Gibbons-Hawking ansatz over a wedge

We give a new construction of Ricci-flat self-dual metrics which is a natural extension of the Gibbons--Hawking ansatz. We also give characterisations of both these constructions, and explain how they come from harmonic morphisms.

We prove an existence theorem for Asymptotically Conical Ricci Flat Kahler metrics in $\mathbb{C}^2$ with cone singularities along a smooth complex curve. These metrics are expected to arise as blow up limits of non collapsed sequences of…

We construct Ricci flat Kahler metrics with cone singularities along a complex hypersurface. This construction is inspired in part by R. Mazzeo's program in the case of negative Einstein constant, and uses the linear theory developed…

We use a generalization of the Gibbons-Hawking ansatz to study the behavior of certain non-compact Calabi-Yau manifolds in the large complex structure limit. This analysis provides an intermediate step toward proving the metric collapse…

We derive a local ansatz for generalized K\"ahler surfaces with nondegenerate Poisson structure and a biholomorphic $S^1$ action which generalizes the classic Gibbons-Hawking ansatz for invariant hyperK\"ahler manifolds, and allows for the…

Given a weighted line arrangement in the projective plane, with weights satisfying natural constraint conditions, we show the existence of a Ricci-flat K\"ahler metric with cone singularities along the lines asymptotic to a polyhedral…

We study the interaction between toric Ricci-flat metrics in dimension 4 and axisymmetric harmonic maps from the 3-dimensional Euclidean space into the hyperbolic plane. Applications include (1). The construction of complete Ricci-flat…

We prove the existence of a Ricci flat metric on the Kummer K3 surface. The proof follows the general strategy of Donaldson's gluing construction. However, we tackle the analysis without appealing to weighted norms or conformal…

In this paper we prove that there exists a compact perturbation of the Ricci flat Taub-Bolt metric that evolves under the Ricci flow into a finite time singularity modelled on the shrinking solition FIK [5]. Moreover, this perturbation can…

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…

In this note we use the Calabi ansatz, in the context of metrics with conical singularities along a divisor, to produce regular Calabi-Yau cones and K\"ahler-Einstein metrics of negative Ricci with a cuspidal point. As an application, we…

An examples of the Ricci-flat metric associated with the equations of Navier-Stokes are constructed. Their properties are investigated.

An examples of a Ricci-flat of four-dimensional spaces with a Walker metrics and their generalizations are constructed. The properties of corresponding geodesic equations are discussed.

In this paper, we study the existence of Poisson metrics on flat vector bundles over noncompact Riemannian manifolds and discuss related consequence, specially on the applications in Higgs bundles, towards generalizing…

We construct a class of complete non-flat Calabi-Yau metrics on C^{N+1} for every N >= 3, which generalize the Taub-NUT metrics from C^2 and C^3 and whose tangent cone at infinity is R^N. The construction relies on the generalized…

We obtain general results on the dynamics of exactly conical geometries, where we use the notion of boundaries at infinity to characterize asymptotic behavior. As we demonstrate in examples, these notions also apply to smooth geometries…

In this short note, we prove that the space of all admissible piecewise linear metrics parameterized by length square on a triangulated manifolds is a convex cone. We further study Regge's Einstein-Hilbert action and give a much more…

We describe a quaternionic-based Ansatz generalizing the Gibbons-Hawking Ansatz to a class of hyperk\"ahler metrics with hidden symmetries. We then apply it to obtain explicit expressions for gravitational instanton metrics of type $D_k$.

Motivated by $G_2$-manifolds with coassociative fibrations in the adiabatic limit, Donaldson and Scaduto conjectured the existence of associative submanifolds homeomorphic to a three-holed $3$-sphere with three asymptotically cylindrical…

Ricci-flat metrics of the ultrahyperbolic signature which enjoy the l-conformal Galilei symmetry are constructed. They involve the AdS_2-metric in a way similar to the near horizon black hole geometries. The associated geodesic equations…