凯勒势空间中大地线的度量下限估计

The Journal of Geometric Analysis Pub Date : 2024-05-12 DOI:10.1007/s12220-024-01654-1

Jingchen Hu

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摘要

在本文中，我们为退化复 Monge-Ampère 方程解的复 Hessian 的第二最小特征值建立了一个正下限估计。因此，我们发现在凯勒势空间中，在（C^2\）规范下相互靠近的任何两点都可以通过一条大地线连接起来，而沿着这条大地线的相关度量不会退化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A Metric Lower Bound Estimate for Geodesics in the Space of Kähler Potentials

In this paper, we establish a positive lower bound estimate for the second smallest eigenvalue of the complex Hessian of solutions to a degenerate complex Monge–Ampère equation. As a consequence, we find that in the space of Kähler potentials any two points close to each other in \(C^2\) norm can be connected by a geodesic along which the associated metrics do not degenerate.

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The Journal of Geometric Analysis

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