9 papers
Kähler-Ricci Tangent Flows in the Analytic Minimal Model Program
Longteng Chen, Max Hallgren, Lucas Lavoyer
We describe certain finite-time singularities of the Kähler-Ricci flow arising in the analytic minimal model program. Assuming that convergence to an asymptotically conical Kähler-…
Singular Kähler--Ricci shrinkers and polarized Fano fibrations
Max Hallgren, Junsheng Zhang
We prove that any singular Kähler--Ricci shrinker arising as a noncollapsed limit of Kähler--Ricci flows admits a natural structure of a polarized Fano fibration. We also show…
Expanding Soliton Models for Kähler-Ricci Flow Near Conical Singularities
Longteng Chen, Max Hallgren, Lucas Lavoyer
Let be a compact analytic space with a finite number of singular points, where the metric at each singular point is modelled on a Kähler cone with smooth canonical model.…
Tangent Flows of Kähler Metric Flows
Max Hallgren, Wangjian Jian
We improve the description of -limits of noncollapsed Ricci flows in the Kähler setting. In particular, the singular strata of such metric flows satisfy…
Canonical surgeries in rotationally invariant Ricci flow
Timothy Buttsworth, Maximilien Hallgren, Yongjia Zhang
We construct a rotationally invariant Ricci flow through surgery starting at any closed rotationally invariant Riemannian manifold. We demonstrate that a sequence of such Ricci flo…
Ricci Flow with Ricci Curvature and Volume Bounded Below
Max Hallgren
We show that a simply-connected closed four-dimensional Ricci flow whose Ricci curvature is uniformly bounded below and whose volume does not approach zero must converge to a $C^{0…
The Entropy of Ricci Flows with Type-I Scalar Curvature Bounds
Max Hallgren
In this paper, we extend the theory of Ricci flows satisfying a Type-I scalar curvature condition at a finite-time singularity. In [Bam16], Bamler showed that a Type-I rescaling pr…
Local Stability of Einstein Metrics Under the Ricci Iteration
Timothy Buttsworth, Maximilien Hallgren
We provide a sufficient condition for the local stability of closed Einstein manifolds of positive Ricci curvature under the Ricci iteration in terms of the spectrum of the Lichner…
The Nonexistence of Noncompact Type-I Ancient 3-d -Solutions of Ricci Flow with Positive Curvature
Max Hallgren
In this short paper, we show there do not exist three-dimensional noncompact -solutions of Ricci flow that have positive curvature and satisfy a Type-I bound. This represents pr…