On a class of fully nonlinear elliptic equations on Hermitian manifolds

By Bo Guan, Weiling Sun. Calculus of Variations and Partial Differential Equations, 2013

61 citations recorded by the source corpus.

We derive a prioriC2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^2$$\end{document} estimates for a class of complex Monge-Ampère type equations on Hermitian manifolds. As an application we solve the Dirichlet problem for these equations under the assumption of existence of a subsolution; the existence result, as well as the second order boundary estimates, is new even for bounded domains in Cn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {C}}^n$$\end{document}.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c3f675b86524d7a9922861b30125a18002249424

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

On Bismut flat manifolds (2016, unknown): “We refer the readers to [37], [9], [10], [11], [12], [13], [24], [41], [19], [16], [17], [18], [33], [34], [35], [36], [25], [26], [27], [39], [40], [38] and the references therein for some recent progress in this area.”
On Curvature Tensors of Hermitian Manifolds (2016, unknown): “See for instance the work of Fu-Yau [5], Fu-Li-Yau [6], Fu [4], Fu-Wang-Wu [7], [8], Liu-Yang [16], [17], [18], Streets-Tian [20], Tosatti-Weinkove [24], [22], Guan-Sun [13], and the references therein.”
Fully non-linear elliptic equations on compact Hermitian manifolds (2015, methodology): “nnian case, and the same proof works in the Hermitian case too. The diﬃculty is that one needs extra conditions to ensure that we have a subsolution along the whole continuity path (see also Guan-Sun [21] for such results in the case of the inverse σk equation). The source of this diﬀerence between ”
Second order estimates for Hessian type fully nonlinear elliptic equations on Riemannian manifolds (2014, unknown): “[9] who extended the result of [38] to f = (σn/σk) 1 n−k for 1 ≤ k ≤ n − 1; see also [16–18].”
Concavity of the Lagrangian phase operator and applications (2016, methodology): “d one assumes instead the existence of an admissible subsolution. This idea was subsequently extended to Riemannian manifolds with boundary [11, 12], Monge-Amp`ere type equations on complex manifolds [10, 14, 15], and to a class of fully non-linear elliptic equations deﬁned on domains in Cn [26], to”