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# Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

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1435-5345
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Volume 2018, Issue 744

# On the long time behaviour of the conical Kähler–Ricci flows

Xiuxiong Chen
/ Yuanqi Wang
Published Online: 2016-03-01 | DOI: https://doi.org/10.1515/crelle-2015-0103

## Abstract

We prove that the conical Kähler–Ricci flows introduced in [11] exist for all time $t\in \left[0,+\mathrm{\infty }\right)$. These immortal flows possess maximal regularity in the conical category. As an application, we show if the twisted first Chern class ${C}_{1,\beta }$ is negative or zero, the corresponding conical Kähler–Ricci flows converge to Kähler–Einstein metrics with conical singularities exponentially fast. To establish these results, one of our key steps is to prove a Liouville-type theorem for Kähler–Ricci flat metrics (which are defined over ${ℂ}^{n}$) with conical singularities.

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Revised: 2015-09-11

Published Online: 2016-03-01

Published in Print: 2018-11-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2018, Issue 744, Pages 165–199, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102,

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