Unique continuation at infinity for conical Ricci expanders

TL;DR

This paper proves unique continuation properties at infinity for asymptotically Ricci flat Ricci expanders by establishing Carleman inequalities for the weighted Laplacian, revealing obstructions related to the asymptotic cone.

Contribution

It introduces Carleman inequalities for the weighted Laplacian on Ricci expanders and demonstrates unique continuation at infinity, highlighting the role of asymptotic cone obstructions.

Findings

Unique continuation at infinity for Ricci expanders

Carleman inequalities for weighted Laplacian established

Obstruction characterized by symmetric 2-tensor on the cone link

Abstract

We establish Carleman inequalities for the weighted laplacian associated to an expanding gradient Ricci soliton. As a consequence, a unique continuation at infinity is proved for asymptotically Ricci flat Ricci expanders. The obstruction at infinity is a symmetric 2-tensor defined on the link of the corresponding asymptotic cone.