STABILITY AND HOLDER REGULARITY OF SOLUTIONS TO COMPLEX MONGE-AMPERE EQUATIONS ON COMPACT HERMITIAN MANIFOLDS

被引：0
作者：
Lu, Chinh H. [1 ]
Trong-Thuc Phung [2 ]
Tat-Dat To [3 ,4 ]
机构：
[1] Univ Paris Saclay, CNRS, Lab Math Orsay, F-91405 Orsay, France
[2] Ho Chi Minh City Univ Technol, VNU HCM, Ho Chi Minh City, Vietnam
[3] Univ Toulouse, Ecole Natl Aviat Civile, 7 Ave Edouard Belin, FR-31055 Toulouse 04, France
[4] Sorbonne Univ, Inst Math Jussieu Paris Rive Gauche, Campus Pierre & Marie Curie,4 Pl Jussieu, F-75252 Paris 05, France
来源：
ANNALES DE L INSTITUT FOURIER | 2021年 / 71卷 / 05期
关键词：
Hermitian manifold; Complex Monge-Ampere equation; Stability; Comparison principle; ENVELOPES; CURRENTS;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let ( X, omega) be a compact Hermitian manifold. We establish a stability result for solutions to complex Monge-Ampere equations with right-hand side in L-p, p > 1. Using this we prove that the solutions are Holder continuous with the same exponent as in the Kahler case by Demailly-Dinew-Guedj-KolodziejPham-Zeriahi. Our techniques also apply to the setting of big cohomology classes on compact Kahler manifolds.
引用
收藏
页码：2019 / 2045
页数：27
相关论文
共 57 条
  • [11] Chen XX, 2015, Arxiv, DOI arXiv:1506.06423
  • [12] Chen XX, 2017, Arxiv, DOI [arXiv:1712.06697, DOI 10.1090/JAMS/967]
  • [13] Chen XX, 2018, Arxiv, DOI arXiv:1801.05907
  • [14] Chen XX, 2018, Arxiv, DOI arXiv:1801.00656
  • [15] Chen XX, 2015, J AM MATH SOC, V28, P183
  • [16] CHERRIER P, 1987, B SCI MATH, V111, P343
  • [17] Chiose I, 2016, Arxiv, DOI arXiv:1609.05945
  • [18] Optimal regularity of plurisubharmonic envelopes on compact Hermitian manifolds
    Chu, Jianchun
    Zhou, Bin
    [J]. SCIENCE CHINA-MATHEMATICS, 2019, 62 (02) : 371 - 380
  • [19] Darvas T, 2019, Arxiv, DOI arXiv:1909.00839
  • [20] Darvas T, 2020, Arxiv, DOI arXiv:1807.00276
123456