A subsolution theorem for the Monge-Ampère equation over an almost Hermitian manifold
Abstract
Let $\Omega\subseteq M$ be a bounded domain with a smooth boundary $\partial\Omega$, where $(M,J,g)$ is a compact, almost Hermitian manifold. The main result of this paper is to consider the Dirichlet problem for a complex Monge-Ampère equation on $\Omega$. Under the existence of a $C^{2}$-smooth strictly $J$-plurisubharmonic ($J$-psh for short) subsolution, we can solve this Dirichlet problem. Our method is based on the properties of subsolutions which have been widely used for fully nonlinear elliptic equations over Hermitian manifolds.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2021
- arXiv:
- arXiv:2107.00167
- Bibcode:
- 2021arXiv210700167Z
- Keywords:
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- Mathematics - Analysis of PDEs;
- Mathematics - Differential Geometry;
- 32W20;
- 32Q60;
- 35B50;
- 31C10
- E-Print:
- 26 pages. All comments are welcome!