The Dirichlet problem for a complex Monge–Ampère type equation on Hermitian manifolds
The Dirichlet problem for a complex Monge–Ampère type equation on Hermitian manifolds
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DOI：
10.1016/j.aim.2013.07.006
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发表时间：
2012-10
影响因子：
1.7
通讯作者：
Bo Guan;Qun Li
中科院分区：
文献类型：
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作者：
Bo Guan;Qun Li
我们关注厄米特流形上的完全非线性椭圆型方程，并寻找技术工具来克服由于非平凡挠率和一般(非伪凸)边界数据而产生的优先估计的推导困难。我们给出了我们的方法，它适用于更一般的方程，通过考虑一个在许多方面类似于复杂的Monge-Ampère方程但有重要区别的特定方程。我们的工作是因为最近人们对几何问题中复流形上的完全非线性方程越来越感兴趣。
We are concerned with fully nonlinear elliptic equations on Hermitian manifolds and search for technical tools to overcome difficulties in derivinga prioriestimates which arise due to the nontrivial torsion and general (non-pseudoconvex) boundary data. We present our methods, which work for more general equations, by considering a specific equation which resembles the complex Monge–Ampère equation in many ways but with crucial differences. Our work is motivated by recent increasing interests in fully nonlinear equations on complex manifolds from geometric problems.