Einstein metrics with anisotropic boundary behaviour

TL;DR

This paper constructs new complete Einstein metrics on balls with boundary behavior that varies point-by-point, asymptotic to different homogeneous Einstein metrics on solvable groups.

Contribution

It introduces a method to produce Einstein metrics with anisotropic boundary behavior, expanding the class of known Einstein metrics with variable asymptotics.

Findings

New examples of complete Einstein metrics on balls.

Boundary at infinity varies with point, asymptotic to different homogeneous Einstein metrics.

Advances understanding of boundary behaviors in Einstein geometry.

Abstract

We construct new examples of complete Einstein metrics on balls. At each point of the boundary at infinity, the metric is asymptotic to a homogeneous Einstein metric on a solvable group, which varies with the point at infinity.