Uniqueness and short time regularity of the weak Kahler-Ricci flow

被引：17

作者：

Di Nezza, Eleonora ^{[1
]}

Lu, Chinh H. ^{[2
,3
]}

机构：

[1] Imperial Coll London, Dept Math, London SW7 2AZ, England

[2] Chalmers, Math Sci, S-41296 Gothenburg, Sweden

[3] Univ Paris 11, Fac Sci Orsay, Dept Math, Bur 144,Baiment 425, F-91405 Orsay, France

来源：

ADVANCES IN MATHEMATICS | 2017年 / 305卷

关键词：

Kahler-Ricci flow; Monge-Ampere equation; Lelong number; Quasi plurisubharmonic function; Generalized capacity; MONGE-AMPERE EQUATION; CONTRACTING EXCEPTIONAL DIVISORS; CLOSED POSITIVE CURRENTS; PLURISUBHARMONIC-FUNCTIONS; EINSTEIN METRICS; MANIFOLDS; CURVATURE; SETS;

D O I：

10.1016/j.aim.2016.10.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X be a compact KOhler manifold. We prove that the Kahler-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. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：953 / 993

页数：41

共 41 条

[1]

[Anonymous], ARXIV14015432

[2]

[Anonymous], PREPRINT

[3] A NEW CAPACITY FOR PLURISUBHARMONIC-FUNCTIONS [J].

BEDFORD, E ;

TAYLOR, BA .

ACTA MATHEMATICA, 1982, 149 (1-2) :1-40

[4]

Berndtsson B., 2016, P AB S IN PRESS

[5] On regularization of plurisubharmonic functions on manifolds [J].

Blocki, Zbigniew ;

Kolodziej, Slawomir .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 135 (07) :2089-2093

[6] An Introduction to the Kahler-Ricci Flow Introduction [J].

Boucksom, Sebastien ;

Eyssidieux, Philippe ;

Guedj, Vincent .

INTRODUCTION TO THE KAHLER-RICCI FLOW, 2013, 2086 :1-6

[7]

Byssidieux P., 2009, J AM MATH SOC, V22, P607

[8]

Campana F, 2013, ANN SCI ECOLE NORM S, V46, P879

[9] DEFORMATION OF KAHLER METRICS TO KAHLER-EINSTEIN METRICS ON COMPACT KAHLER-MANIFOLDS [J].

CAO, HD .

INVENTIONES MATHEMATICAE, 1985, 81 (02) :359-372

[10] ON THE WEAK KAHLER-RICCI FLOW [J].

Chen, X. X. ;

Tian, G. ;

Zhang, Z. .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 363 (06) :2849-2863

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