Expanding Soliton Models for K\"ahler-Ricci Flow Near Conical Singularities

Longteng Chen; Max Hallgren; Lucas Lavoyer

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arXiv · 2604.04223

Expanding Soliton Models for K\"ahler-Ricci Flow Near Conical Singularities

Longteng Chen·Max Hallgren·Lucas Lavoyer

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Abstract

Let $(Y,g_0)$ be a compact analytic space with a finite number of singular points, where the metric at each singular point is modelled on a K\"ahler cone with smooth canonical model. We show that the K\"ahler-Ricci flow with such initial data satisfies a $C/t$ curvature bound, and that the flow near each singular point is modelled on the unique K\"ahler-Ricci expander asymptotic to the corresponding cone. Our motivation is to give a geometric description of the K\"ahler--Ricci flow emerging from singularities arising in the analytic minimal model program.

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BibTeX RIS

Longteng Chen, Max Hallgren, Lucas Lavoyer. 2026-04-05. Expanding Soliton Models for K\"ahler-Ricci Flow Near Conical Singularities. https://arxiv.org/abs/2604.04223

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