Extremal metrics on toric surfaces

被引：9
作者：
Chen, Bohui
Li, An-Min
Sheng, Li
机构：
来源：
ADVANCES IN MATHEMATICS | 2018年 / 340卷
关键词：
Abreu equations; Toric surfaces; Extrernal metrics; SCALAR CURVATURE; KAHLER GEOMETRY; K-STABILITY;
D O I：
10.1016/j.aim.2018.10.015
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the Abreu equation on toric surfaces with prescribed scalar curvatures on Delzant polytope. In particular, we prove the existence of the extremal metric when relative K-stability is assumed. (C) 2018 Elsevier Inc. All rights reserved.
引用
收藏
页码：363 / 405
页数：43
相关论文
共 33 条
[1]   Kahler geometry of toric varieties and extremal metrics [J].
Abreu, M .
INTERNATIONAL JOURNAL OF MATHEMATICS, 1998, 9 (06) :641-651
[2]   Hamiltonian 2-forms in Kahler geometry, III Extremal metrics and stability [J].
Apostolov, Vestislav ;
Calderbank, DavidM. J. ;
Gauduchon, Paul ;
Tonnesen-Friedman, Christina W. .
INVENTIONES MATHEMATICAE, 2008, 173 (03) :547-601
[3]  
CALABI E, 1982, ANN MATH STUD, P259
[4]  
Chen B. H., ARXIV10082606
[5]   Interior regularity on the Abreu equation [J].
Chen, Bo Hui ;
Li, An-Min ;
Sheng, Li .
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2013, 29 (01) :33-38
[6]   Uniform K-stability for extremal metrics on tone varieties [J].
Chen, Bohui ;
Li, An-Min ;
Sheng, Li .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 257 (05) :1487-1500
[7]   The Abreu equation with degenerated boundary conditions [J].
Chen, Bohui ;
Li, An-Min ;
Sheng, Li .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (10) :5235-5259
[8]   Geometry of Kahler metrics and foliations by holomorphic discs [J].
Chen, X. X. ;
Tian, G. .
PUBLICATIONS MATHEMATIQUES, NO 107, 2008, 107 (107) :1-107
[9]   Uniqueness of extremal Kahler metrics [J].
Chen, XX ;
Tian, G .
COMPTES RENDUS MATHEMATIQUE, 2005, 340 (04) :287-290
[10]   PERIODIC HAMILTONIANS AND CONVEX IMAGES OF MOMENTUM MAPPING [J].
DELZANT, T .
BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 1988, 116 (03) :315-339
1234