Regularizing property of the twisted conical K\"ahler-Ricci flow
Jiawei Liu, Shiyu Zhang, Xi Zhang
TL;DR
This paper proves the regularity and uniqueness of the twisted conical Kähler-Ricci flow starting from a positive current with zero Lelong number, extending known smooth flow results to conical singularities.
Contribution
It extends the regularizing and uniqueness properties of the twisted Kähler-Ricci flow to cases with conical singularities, broadening the understanding of such flows.
Findings
Proves regularity of the flow with conical singularities.
Establishes uniqueness of the flow in this setting.
Extends existing theorems to more singular cases.
Abstract
In this paper, we show the regularity and uniqueness of the twisted conical K\"ahler-Ricci flow running from a positive closed current with zero Lelong number, which extends the regularizing property of the smooth twisted K\"ahler-Ricci flow, known as Guedj-Zeriahi's existence theorem and Di Nezza-Lu's uniqueness theorem, to the conical singularity case.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Black Holes and Theoretical Physics