In this paper, we study the stability of the conical Kahler-Ricci flows on Fano manifolds. That is, if there exists a conical Kahler-Einstein metric with cone angle $2\pi\beta$ along the divisor, then for any $\beta'$ sufficiently close to $\beta$, the corresponding conical Kahler-Ricci flow converges to a conical Kahler-Einstein metric with cone angle $2\pi\beta'$ along the divisor. Here, we only use the condition that the Log Mabuchi energy is bounded from below. This is a weaker condition than the properness that we have adopted to study the convergence before. As corollaries, we give parabolic proofs of Donaldson's openness theorem and his existence conjecture for the conical Kahler-Einstein metrics with positive Ricci curvatures.

中文翻译：

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Fano 流形上锥形 Kähler-Ricci 流的稳定性

在本文中，我们研究了 Fano 流形上锥形 Kahler-Ricci 流的稳定性。也就是说，如果沿着除数存在锥角为 $2\pi\beta$ 的锥形 Kahler-Einstein 度量，那么对于任何足够接近 $\beta$ 的 $\beta'$，对应的锥形 Kahler-Ricci 流收敛到圆锥角为 $2\pi\beta'$ 沿除数的圆锥形 Kahler-Einstein 度量。在这里，我们只使用 Log Mabuchi 能量从下方有界的条件。这是一个比我们之前研究收敛所采用的适当性更弱的条件。作为推论，我们给出了唐纳森的开放性定理的抛物线证明以及他对具有正 Ricci 曲率的圆锥形 Kahler-Einstein 度量的存在猜想。