3 papers
math.DG2026
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…
math.DG2025
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…
math.DG2024
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…