Complete the asymptotic conicity conjecture for Kähler–Ricci shrinkers

Establish the full asymptotic conicity conjecture for tangent spaces at infinity of noncompact Kähler–Ricci shrinkers, beyond the metric-cone structure established in the paper.

Background

The paper studies the geometry at infinity of noncompact Kähler–Ricci shrinkers. It proves that every such shrinker has a unique tangent cone at infinity and that the limiting space is a metric cone naturally identified with the base of the associated polarized Fano fibration.

The authors explicitly state that their metric-cone result proves only part of an asymptotic conicity conjecture previously formulated by Sun and Zhang. Thus, the remaining assertions of that conjecture are not resolved by the present work.