The Fu-Yau equation on compact astheno-Kahler manifolds

被引：8
作者：
Chu, Jianchun [1 ]
Huang, Liding [2 ]
Zhu, Xiaohua [3 ]
机构：
[1] Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China
[2] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China
[3] Peking Univ, Sch Math Sci, Yiheyuan Rd 5, Beijing 100871, Peoples R China
来源：
ADVANCES IN MATHEMATICS | 2019年 / 346卷
关键词：
The Fu-Yau equation; Hermitian manifolds; Astheno-Kahler manifolds; 2-nd Hessian equation; NONLINEAR ELLIPTIC-EQUATIONS; 2ND-ORDER ESTIMATE; COMPLEX;
D O I：
10.1016/j.aim.2019.02.006
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the Fu-Yau equation on compact Hermitian manifolds and prove the existence of solutions of equation on astheno-Kaler manifolds. We also prove the uniqueness of solutions of Fu-Yau equation when the slope parameter a is negative. (C) 2019 Elsevier Inc. All rights reserved.
引用
收藏
页码：908 / 945
页数：38
相关论文
共 31 条
  • [1] Chu J., ARXIV180109351
  • [2] Chu J., 2019, J EUR MATH SOC JEMS
  • [3] Chu J., ARXIV170704072
  • [4] LIOUVILLE AND CALABI-YAU TYPE THEOREMS FOR COMPLEX HESSIAN EQUATIONS
    Dinew, Slawomir
    Kolodziej, Slawomir
    [J]. AMERICAN JOURNAL OF MATHEMATICS, 2017, 139 (02) : 403 - 415
  • [5] Astheno-Kahler and Balanced Structures on Fibrations
    Fino, Anna
    Grantcharov, Gueo
    Vezzoni, Luigi
    [J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2019, 2019 (22) : 7093 - 7117
  • [6] On astheno-Kahler metrics
    Fino, Anna
    Tomassini, Adriano
    [J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2011, 83 : 290 - 308
  • [7] Fu JX, 2008, J DIFFER GEOM, V78, P369
  • [8] Fu JX, 2007, COMMUN ANAL GEOM, V15, P29
  • [9] Semilinear equations, the γk function, and generalized Gauduchon metrics
    Fu, Jixiang
    Wang, Zhizhang
    Wu, Damin
    [J]. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2013, 15 (02) : 659 - 680
  • [10] Garcia-Fernandez M., ARXIV160902615
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