Subelliptic estimates from Gromov hyperbolicity
Subelliptic estimates from Gromov hyperbolicity
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发表时间：
2019-04
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通讯作者：
Andrew M. Zimmer
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作者：
Andrew M. Zimmer
在本文中，我们证明：如果有界凸域（没有边界正则性假设）上的完整卡勒-爱因斯坦度量是格罗莫夫双曲，则 $\overline{\partial}$-Neumann 问题满足亚椭圆估计。我们还根据仿射变换组下域的轨道来描述格罗莫夫双曲性。这种特征使我们能够构建许多例子。例如，如果有界凸域上的希尔伯特度量是格罗莫夫双曲型，那么卡勒-爱因斯坦度量也是。
In this paper we prove: if the complete Kahler-Einstein metric on a bounded convex domain (with no boundary regularity assumptions) is Gromov hyperbolic, then the $\overline{\partial}$-Neumann problem satisfies a subelliptic estimate. We also provide a characterization of Gromov hyperbolicity in terms of orbit of the domain under the group of affine transformations. This characterization allows us to construct many examples. For instance, if the Hilbert metric on a bounded convex domain is Gromov hyperbolic, then the Kahler-Einstein metric is as well.