4 papers · 1 filter
Geometry of gravitational instantons
Mingyang Li, Song Sun
We survey recent progress in the classification of hyperkähler and Hermitian gravitational instantons (i.e., complete noncompact 4 dimensional Ricci-flat manifolds with quadratic…
Poincaré-Einstein 4-manifolds with cusps
Mingyang Li, Hongyi Liu
In this paper, we construct Poincaré-Einstein 4-manifolds with various kinds of cusps. In particular, we construct: (1) Infinite families of Einstein metrics on $(0,\infty)\times…
Gravitational instantons and harmonic maps
Mingyang Li, Song Sun
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. Applicatio…
On conical asymptotically flat manifolds
Mingyang Li, Song Sun
We prove a conjecture of Petrunin and Tuschmann on the non-existence of asymptotically flat 4-manifolds asymptotic to the half plane. We also survey recent progress and questions c…