Uniqueness and short time regularity of the weak Kähler-Ricci flow
Journal article, 2017

Let X be a compact Kähler manifold. We prove that the Kähler–Ricci flow starting from arbitrary closed positive (1,1)-currents is smooth outside some analytic subset. This regularity result is optimal, meaning that the flow has positive Lelong numbers for short time if the initial current has. We also prove that the flow is unique when starting from currents with zero Lelong numbers.

Lelong number

Kähler-Ricci flow

Quasi plurisubharmonic function

Generalized capacity

Monge–Ampère equation


Eleonora Di Nezza

Imperial College London

Hoang Chinh Lu

University of Gothenburg

Chalmers, Mathematical Sciences

Advances in Mathematics

0001-8708 (ISSN) 1090-2082 (eISSN)

Vol. 305 953-993

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