论文标题
Sibony Metric和Bergman内核的生长范围较低
Growth of Sibony metric and Bergman kernel for domains with low regularity
论文作者
论文摘要
结果表明，即使有$ \ Mathcal C^1 $边界的任何有限的非伪有核心域的弱多维Suta猜想都失败了：伯格曼内核的乘积按Azukawa Metric的Inideatrix的体积不限制下面。这是通过找到一个方向而获得的，该方向沿着偶性度量倾向于无穷大，因为基点趋向于边界。 Lipschitz边界的类似陈述失败了。对于一般的$ \ Mathcal C^1 $边界，我们就某些定向距离功能进行了sibony指标的估计。对于有界的伪共元结构域，Blocki-Zwonek Suita型定理意味着伯格曼内核的无穷大的生长； S. Fu在$ \ Mathcal c^2 $ case中证明，伯格曼内核作为距离距离距离的正方形的事实扩展到具有Lipschitz边界的有界的pseudoconvex域。
It is shown that even a weak multidimensional Suita conjecture fails for any bounded non-pseudoconvex domain with $\mathcal C^1$ boundary: the product of the Bergman kernel by the volume of the indicatrix of the Azukawa metric is not bounded below. This is obtained by finding a direction along which the Sibony metric tends to infinity as the base point tends to the boundary. The analogous statement fails for a Lipschitz boundary. For a general $\mathcal C^1$ boundary, we give estimates for the Sibony metric in terms of some directional distance functions. For bounded pseudoconvex domains, the Blocki-Zwonek Suita-type theorem implies growth to infinity of the Bergman kernel; the fact that the Bergman kernel grows as the square of the reciprocal of the distance to the boundary, proved by S. Fu in the $\mathcal C^2$ case, is extended to bounded pseudoconvex domains with Lipschitz boundaries.
