Fully nonlinear elliptic equations with gradient terms on compact almost Hermitian manifolds

被引：0
作者：
Liding Huang
Jiaogen Zhang
机构：
[1] Westlake Institute for Advanced Study (Westlake University),School of Mathematical Sciences
[2] University of Science and Technology of China,undefined
来源：
Mathematische Zeitschrift | 2023年 / 303卷
关键词：
Fully nonlinear elliptic equations; Almost Hermitian manifolds; Monge-Ampère equation; Deformed Hermitian-Yang-Mills equation;
D O I：
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学科分类号：
摘要：
We establish second order estimates for a general class of fully nonlinear elliptic equations with gradient terms on almost Hermitian manifolds including the deformed Hermitian-Yang-Mills equation and the equation in the proof of Gauduchon conjecture by Székelyhidi-Tosatti-Weinkove. As applications, we also consider the existence of Monge-Ampère  equation and Hessian equations.
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[1]  
Andrews B(1994)Contraction of convex hypersurfaces in Euclidean space Calc. Var. Partial Differ. Equ. 2 151-171
[2]  
Błocki Z(2005)On uniform estimate in Calabi-Yau theorem Sci. China Ser. A 48 244-247
[3]  
Błocki Z(2011)On the uniform estimate in the Calabi-Yau theorem II. Sci. China Math. 54 1375-1377
[4]  
Cherrier P(1987)Équations de Monge-Ampère sur les variétés Hermitiennes compactes Bull. Sc. Math. (2) 111 343-385
[5]  
Chu J(2021)Fully nonlinear degenerate elliptic equations in complex geometry J. Funct. Anal. 281 45-1984
[6]  
McCleerey N(2019)The Monge-Ampère equation for non-integrable almost complex structures J. Eur. Math. Soc. (JEMS) 21 1949-89
[7]  
Chu J(2017)Concavity of the Lagrangian phase operator and applications Calc. Var. Partial Differ. Equ. 56 56-452
[8]  
Tosatti V(2020)(1,1) forms with specified Lagrangian phase: a priori estimates and algebraic obstructions Camb. J. Math. 8 407-415
[9]  
Weinkove B(2017)Liouville and Calabi-Yau type theorems for complex Hessian equations Amer. J. Math. 139 403-332
[10]  
Collins T(1989)Immersed hypersurfaces with constant Weingarten curvature Math. Ann. 283 329-903
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