AI 中文总结
研究复流形紧子集上全纯函数相关紧集的度量熵，通过确定其渐近性量化紧性，为\(\mathbb{C}^n\)中区域的柯尔莫哥洛夫问题提供新解并推广到任意斯坦流形区域。
AI 中文摘要
根据蒙泰尔定理，在复流形的紧子集上那些能全纯延拓到该流形且一致有界的连续函数，在一致拓扑下构成一个紧集。我们通过确定相关度量熵的渐近性来量化这种紧性，从而为\(\mathbb{C}^n\)中区域的一个柯尔莫哥洛夫问题给出新解，并将该解推广到任意斯坦流形中的区域。
英文摘要
By Montel's theorem, the continuous functions on a compact subset of a complex manifold that admit uniformly bounded holomorphic extensions to the manifold form a compact set in the uniform topology. We render this compactness quantitative by determining the asymptotics of the associated metric entropy, thereby giving a new solution to a problem of Kolmogorov for domains in $\mathbb{C}^n$ and extending the solution to domains in arbitrary Stein manifolds.
