Maximal time existence of unnormalized conical Kähler-Ricci flow

Liangming Shen

doi:10.1515/crelle-2018-0007

Maximal time existence of unnormalized conical Kähler-Ricci flow

Liangming Shen^*

^*Corresponding author for this work

University of British Columbia

Research output: Contribution to journal › Review article › peer-review

4 Scopus citations

Abstract

We generalize the maximal time existence of Kähler-Ricci flow in [G. Tian and Z. Zhang, On the Kähler-Ricci flow on projective manifolds of general type, Chin. Ann. Math. Ser. B 27 (2006), no. 2, 179-192] and [J. Song and G. Tian, The Kähler-Ricci flow through singularities, Invent. Math. 207 (2017), no. 2, 519-595] to the conical case. Furthermore, if the log canonical bundle K_M + (1-β) is big or big and nef, we can examine the limit behaviors of such conical Kähler-Ricci flow. Moreover, these results still hold when D is a simple normal crossing divisor.

Original language	English
Pages (from-to)	169-193
Number of pages	25
Journal	Journal fur die Reine und Angewandte Mathematik
Volume	2020
Issue number	760
DOIs	https://doi.org/10.1515/crelle-2018-0007
State	Published - 1 Mar 2020
Externally published	Yes

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title = "Maximal time existence of unnormalized conical K{\"a}hler-Ricci flow",

abstract = "We generalize the maximal time existence of K{\"a}hler-Ricci flow in [G. Tian and Z. Zhang, On the K{\"a}hler-Ricci flow on projective manifolds of general type, Chin. Ann. Math. Ser. B 27 (2006), no. 2, 179-192] and [J. Song and G. Tian, The K{\"a}hler-Ricci flow through singularities, Invent. Math. 207 (2017), no. 2, 519-595] to the conical case. Furthermore, if the log canonical bundle KM + (1-β) is big or big and nef, we can examine the limit behaviors of such conical K{\"a}hler-Ricci flow. Moreover, these results still hold when D is a simple normal crossing divisor.",

author = "Liangming Shen",

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year = "2020",

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doi = "10.1515/crelle-2018-0007",

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AU - Shen, Liangming

PY - 2020/3/1

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N2 - We generalize the maximal time existence of Kähler-Ricci flow in [G. Tian and Z. Zhang, On the Kähler-Ricci flow on projective manifolds of general type, Chin. Ann. Math. Ser. B 27 (2006), no. 2, 179-192] and [J. Song and G. Tian, The Kähler-Ricci flow through singularities, Invent. Math. 207 (2017), no. 2, 519-595] to the conical case. Furthermore, if the log canonical bundle KM + (1-β) is big or big and nef, we can examine the limit behaviors of such conical Kähler-Ricci flow. Moreover, these results still hold when D is a simple normal crossing divisor.

AB - We generalize the maximal time existence of Kähler-Ricci flow in [G. Tian and Z. Zhang, On the Kähler-Ricci flow on projective manifolds of general type, Chin. Ann. Math. Ser. B 27 (2006), no. 2, 179-192] and [J. Song and G. Tian, The Kähler-Ricci flow through singularities, Invent. Math. 207 (2017), no. 2, 519-595] to the conical case. Furthermore, if the log canonical bundle KM + (1-β) is big or big and nef, we can examine the limit behaviors of such conical Kähler-Ricci flow. Moreover, these results still hold when D is a simple normal crossing divisor.

UR - https://www.scopus.com/pages/publications/85046939343

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DO - 10.1515/crelle-2018-0007

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VL - 2020

SP - 169

EP - 193

JO - Journal fur die Reine und Angewandte Mathematik

JF - Journal fur die Reine und Angewandte Mathematik

IS - 760

ER -

Maximal time existence of unnormalized conical Kähler-Ricci flow

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