We derive quantitative boundary estimates, and then solve the Dirichlet problem for a general class of fully non-linear elliptic equations on annuli of Kähler cones over closed Sasakian manifolds. This extends extensively a result concerning the geodesic equations in the space of Sasakian metrics due to Guan–Zhang. Our results show that the solvability is deeply affected by the transverse Kähler structures of Sasakian manifolds. We also discuss possible extensions of the results to equations with right-hand side depending on unknown solutions.

中文翻译：

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Kähler锥上的完全非线性椭圆方程的正则性

我们导出定量边界估计，然后在封闭的Sasakian流形上的Kähler锥环上求解一类完全非线性椭圆方程的一般Dirichlet问题。这广泛地扩展了有关关张的Sasakian度量空间中的测地线方程的结果。我们的结果表明，Sasakian流形的横向Kähler结构严重影响了可溶性。我们还讨论了将结果扩展到方程右侧的方程的可能性，具体取决于未知的解决方案。