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arXiv · 2607.08325

Geometric smoothing by the K\"ahler-Ricci Flow

Eleonora Di Nezza·Vincent Guedj·Chinh Hoang Lu
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Abstract

We study the geometric regularization of a positive closed current by the (twisted) K\"ahler-Ricci flow on a compact K\"ahler manifold. We conjecture that the local Arnold multiplicities linearly decrease to zero, while the flow produces complete K\"ahler metrics in the Zariski open subset of points that have small Lelong numbers. We prove this conjecture in complex dimension 1 and provide several partial results in higher dimension.

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Eleonora Di Nezza, Vincent Guedj, Chinh Hoang Lu. 2026-07-09. Geometric smoothing by the K\"ahler-Ricci Flow. https://arxiv.org/abs/2607.08325

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