A Priori Estimates for Complex Monge–Ampère Equation on Hermitian Manifolds

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The Monge-Ampère equation for (n − 1)-plurisubharmonic functions on a compact Kähler manifold (2013, methodology): “11) (ω + √ −1∂∂u) ∧ ω = eω, for fixed 2 6 k 6 n− 1, was proved by Dinew-Ko lodziej [11], who used the second order estimate of Hou-Ma-Wu [31] (see also [3, 10, 30, 32, 33, 34, 36, 39, 59] for earlier and related work on these equations).”
The Monge–Ampère equation for non-integrable almost complex structures (2016, background): “1) has a unique solution for ω Hermitian, up to adding a (unique) constant to F (see also [45, 24], as well as [4, 9, 14, 29, 30, 32, 35, 40, 49, 57, 58] for later developments).”
A second order estimate for general complex Hessian equations (2015, background): “1708 DUONG H. PHONG, SEBASTIEN PICARD AND XIANGWEN ZHANG Acknowledgements The authors would like to thank Pengfei Guan for stimulating conversations and for sharing his unpublished notes.”
Gauduchon metrics with prescribed volume form (2015, background): “Some other works on this topic include [6, 7, 13, 14, 15, 16, 21, 22, 23, 25, 26, 30, 31, 39, 40, 42, 43, 44].”