Extending recent work in 5 dimensions, we prove the existence and uniqueness of solutions
to the reduced Einstein equations for vacuum black holes in (n+ 3)-dimensional spacetimes …

In this paper a lower bound for the ADM mass is given in terms of the angular momenta and
charges of black holes present in axisymmetric initial data sets for the Einstein–Maxwell …

We study the problem of stationary bi-axially symmetric solutions of the $5 $-dimensional
minimal supergravity equations. Essentially all possible solutions with nondegenerate …

Motivated by stationary vacuum solutions of the Einstein field equations, we study singular
harmonic maps from domains of 3-dimensional Euclidean space to the hyperbolic plane …

One potential pathway to find an ultimate rule governing our universe is to hunt for a
connection among the fundamental equations in physics. Recently, Ren et al. reported that …

General relativity and quantum mechanism are two separate rules of modern physics
explaining how nature works. Both theories are accurate, but the direct connection between …

We provide a systematic convergence analysis of the Hessian operator estimator from
random samples supported on a low dimensional manifold. We show that the impact of the …

This paper presents a general existence and uniqueness result for harmonic maps with
prescribed singularities into non-positively curved targets, and surveys a number of …

We show that a stationary asymptotically flat electro-vacuum solution of Einstein's equations
that is everywhere locally “almost isometric” to a Kerr–Newman solution cannot admit more …

In recent works a method was developed which uses harmonic maps to construct stationary
asymptotically flat solutions to the (4+ 1)-dimensional vacuum Einstein equations with …