On the continuity of half-plane capacity with respect to Carath\'eodory convergence
On the continuity of half-plane capacity with respect to Carath\'eodory convergence
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DOI：
10.1007/978-981-19-4672-1_20
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发表时间：
2021-06
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影响因子：
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通讯作者：
Takuya Murayama
中科院分区：
文献类型：
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作者：
Takuya Murayama
我们研究了半平面容量作为边界壳的函数相对于Carathéodory收敛的连续性。特别是，我们感兴趣的是船体是无界的。在假设每个船体都包含在有限虚部和有限半平面容量的固定船体中的情况下，我们证明了半平面容量确实是连续的。我们还讨论了这一结果在基础域是有限连通的情况下的推广。
We study the continuity of half-plane capacity as a function of boundary hulls with respect to the Carathéodory convergence. In particular, our interest lies in the case that hulls are unbounded. Under the assumption that every hull is contained in a fixed hull with finite imaginary part and finite half-plane capacity, we show that the half-plane capacity is indeed continuous. We also discuss the extension of this result to the case that the underlying domain is finitely connected.