9 papers
Finite time singularities of the Ricci flow on compact Kähler surfaces are of Type I
Charles Cifarelli, Ronan Conlon, Max Hallgren +1
For any volume-collapsing finite-time singularity of a Kähler-Ricci flow on a compact Kähler surface, we show the flow satisfies a Type I curvature bound and classify the correspon…
Structure Theory of Parabolic Nodal and Singular Sets
Max Hallgren, Robert Koirala, Zilu Ma
We establish new estimates for the size and structure of the nodal set and the singular set of solutions to parabolic inequalities with parabolic…
An -Regularity Theorem for Non-collapsed Ricci Flow
Harry Fluck, Max Hallgren
In this article we prove an -regularity theorem for non-collapsed Ricci flows, and use this to prove new estimates for singularity models of Fano Kähler-Ricci flows. In the cour…
Remarks on Singular Kähler-Einstein Metrics
Max Hallgren, Gábor Székelyhidi
We study two different natural notions of singular Kähler-Einstein metrics on normal complex varieties. In the setting of singular Ricci flat Kähler cone metrics that arise as non-…
On Kähler-Einstein Currents
Yifan Chen, Shih-Kai Chiu, Max Hallgren +3
We show that a general class of singular Kähler metrics with Ricci curvature bounded below define Kähler currents. In particular the result applies to singular Kähler-Einstein metr…
Non-collapsed finite time singularities of the Ricci flow on compact Kähler surfaces are of Type I
Ronan J. Conlon, Max Hallgren, Zilu Ma
We show that any non-collapsed finite time singularity of the Ricci flow on a compact Kähler surface is of Type I. Combined with a previous result of the first author, Cifarelli, a…
Kähler-Ricci Tangent Flows are Infinitesimally Algebraic
Max Hallgren
We show that any tangent cone of a singular shrinking Kähler-Ricci soliton is a normal affine algebraic variety. Moreover, the regular set of such a tangent cone in the metric sens…
Geometric regularity of blow-up limits of the Kähler-Ricci flow
Max Hallgren, Wangjian Jian, Jian Song +1
We establish geometric regularity for Type I blow-up limits of the Kähler-Ricci flow based at any sequence of Ricci vertices. As a consequence, the limiting flow is continuous in t…
A Differential Harnack Inequality for the Newell-Whitehead Equation
Derek Booth, Jack Burkart, Xiaodong Cao +4
This paper will develop a Li-Yau-Hamilton type differential Harnack estimate for positive solutions to the Newell-Whitehead equation on . We then use our LYH-differen…