Fully nonlinear elliptic equations on Hermitian manifolds for symmetric functions of partial Laplacians

Bo Guan; Chunhui Qiu; Mathew George

arxiv: 2110.00490 · v1 · pith:3YW7AEUZnew · submitted 2021-10-01 · 🧮 math.AP · math.CV· math.DG

Fully nonlinear elliptic equations on Hermitian manifolds for symmetric functions of partial Laplacians

Mathew George , Bo Guan , Chunhui Qiu This is my paper

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keywords equationsmanifoldsellipticfullygeneralhermitiannonlinearassumptions

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We consider a class of fully nonlinear second order elliptic equations on Hermitian manifolds closely related to the general notion of $\bfG$-plurisubharmonicity of Harvey-Lawson and an equation treated by Sz\'ekelyhidi-Tosatti-Weinkove in the proof of Gauduchon conjecture. Under fairly general assumptions we derive interior estimates and establish the existence of smooth solutions for the Dirichlet problem as well as for equations on closed manifolds.

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