We study weak geodesics in the space of potentials for the deformed Hermitian–Yang–Mills equation. The geodesic equation can be formulated as a degenerate elliptic equation, allowing us to employ nonlinear Dirichlet duality theory, as developed by Harvey–Lawson. By exploiting the convexity of the level sets of the Lagrangian angle operator in the highest branch, we are able to construct $C^0$ solutions of the associated Dirichlet problem.

中文翻译：

---

变形的 Hermitian-Yang-Mills 方程的弱测地线

我们研究变形的 Hermitian-Yang-Mills 方程在势空间中的弱测地线。测地线方程可以表述为退化椭圆方程，允许我们采用 Harvey-Lawson 开发的非线性 Dirichlet 对偶理论。通过利用最高分支中拉格朗日角算子的水平集的凸性，我们能够构建相关狄利克雷问题的 $C^0$ 解决方案。