光滑边界点附近的局部渐近性与双曲型度量的估计
Local asymptotics near a smooth boundary point and estimates for a hyperbolic-type metric
AI总结：
本文研究双曲型度量$m_D$的局部边界行为，通过边界平坦化技术等方法建立其光滑边界点附近的渐近公式，证明其为某度量量的内度量，最终得到该度量的改进下界。
AI中文摘要：
本文研究新近提出的双曲型度量$m_D$的局部边界行为。首先，利用边界平坦化技术与$m_D$测地线的局部行为，建立其在任意$C^1$光滑边界点附近的渐近公式；接着引入类似Nikolov-Andreev度量的度量量，证明$m_D$是与其关联的内度量；最后通过建立精确的双边比较不等式，得到$m_D$度量的改进下界。
英文摘要：
In this paper, we investigate the local boundary behaviour of a recently developed hyperbolic-type metric $m_D$. First, employing a boundary-flattening technique and local behaviour of $m_D$-geodesics, we establish its asymptotic formula near any $C^1$-smooth boundary point. Next, we introduce a metric quantity analogous to the Nikolov--Andreev metric and show that $m_D$ is the inner metric associated with it. Finally, by establishing a sharp two-sided comparison inequality, we obtain an improved lower bound for the $m_D$-metric.
