AI 中文总结
本文研究广义Monge-Ampère方程的测地线存在性与J-泛函凸性，推广了陈秀雄及Collins-Yau的结果至两个右Noetherian多项式情形。
AI 中文摘要
陈秀雄证明了Kähler势空间中$C^{1, \ar 1}$测地线的存在性，以及$J$-泛函沿$C^{1, \ar 1}$测地线的凸性。Collins和Yau对超临界Leung--Yau--Zaslow方程证明了类似结果。本文中，我们研究与两个处于适当位置的右Noetherian多项式相关的广义Monge--Ampère方程的类似图景。
英文摘要
Xiuxiong Chen proved the existence of $C^{1, \bar 1}$ geodesics in the space of Kähler potentials and the convexity of the $J$-functional along $C^{1, \bar 1}$ geodesics. Analogous results were proved by Collins and Yau for the hypercritical Leung--Yau--Zaslow equation. In this paper, we study a similar picture for generalised Monge--Ampère equations associated with two right-Noetherian polynomials in proper position.
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