The Kähler–Ricci flow through singularities

Jian Song; Gang Tian

doi:10.1007/s00222-016-0674-4

The Kähler–Ricci flow through singularities

Jian Song, Gang Tian

Mathematics

Research output: Contribution to journal › Article › peer-review

70 Scopus citations

Abstract

We prove the existence and uniqueness of the weak Kähler–Ricci flow on projective varieties with log terminal singularities. We also show that the weak Kähler–Ricci flow can be uniquely continued through divisorial contractions and flips if they exist. Finally we propose an analytic version of the minimal model program with Ricci flow.

Original language	English (US)
Pages (from-to)	519-595
Number of pages	77
Journal	Inventiones Mathematicae
Volume	207
Issue number	2
DOIs	https://doi.org/10.1007/s00222-016-0674-4
State	Published - Feb 1 2017

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s00222-016-0674-4

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abstract = "We prove the existence and uniqueness of the weak K{\"a}hler–Ricci flow on projective varieties with log terminal singularities. We also show that the weak K{\"a}hler–Ricci flow can be uniquely continued through divisorial contractions and flips if they exist. Finally we propose an analytic version of the minimal model program with Ricci flow.",

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AB - We prove the existence and uniqueness of the weak Kähler–Ricci flow on projective varieties with log terminal singularities. We also show that the weak Kähler–Ricci flow can be uniquely continued through divisorial contractions and flips if they exist. Finally we propose an analytic version of the minimal model program with Ricci flow.

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The Kähler–Ricci flow through singularities

Abstract

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