In this paper, we consider the $V$-soliton equation which is a degenerate fully nonlinear equation introduced by La Nave and Tian in their work on Kahler-Ricci flow on symplectic quotients. One can apply the interpretation to study finite time singularities of the Kahler-Ricci flow. As in the case of Kahler-Einstein metrics, we can also reduce the $V$-soliton equation to a scalar equation on Kahler potentials, which is of Monge-Ampere type. We formulate some preliminary estimates for such a scalar equation on a compact Kahler manifold $M$.

中文翻译：

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辛商上的标量 V 孤子方程和 Kähler-Ricci 流

在本文中，我们考虑 $V$-孤子方程，它是由 La Nave 和 Tian 在他们关于辛商的 Kahler-Ricci 流的工作中引入的退化完全非线性方程。人们可以应用这种解释来研究 Kahler-Ricci 流的有限时间奇点。与 Kahler-Einstein 度量的情况一样，我们也可以将 $V$-孤子方程简化为 Kahler 势的标量方程，这是 Monge-Ampere 类型。我们在紧致的 Kahler 流形 $M$ 上为这种标量方程制定了一些初步估计。