论文标题
C-转运直径
C-transfinite diameter
论文作者
论文摘要
我们给出了紧凑型套件的$ c- $ transfinite直径$Δ_c（k）$ k \ subset \ subset \ mathbb {c}^2 $，这是单变量compacta的产物，其中$ c \ subset（\ mathbb {r}^+）^+）^2 $是一个侧面。一路走来，我们证明了$δ_c（k）$和$ c- $ robin函数$ρ_{顶点$（0,0），（b，0），（0，a）$。 Finally, we show how the definition of $δ_C(K)$ can be extended to include many nonconvex bodies $C\subset \mathbb{R}^d$ for $d-$circled sets $K\subset \mathbb{C}^d$, and we prove an integral formula for $δ_C(K)$ which we use to compute a formula for the $C-$transfinite Euclidean单位球的直径$ \ MATHBB {B} \ subset \ Mathbb {C}^2 $。
We give a general formula for the $C-$transfinite diameter $δ_C(K)$ of a compact set $K\subset \mathbb{C}^2$ which is a product of univariate compacta where $C\subset (\mathbb{R}^+)^2$ is a convex body. Along the way we prove a Rumely type formula relating $δ_C(K)$ and the $C-$Robin function $ρ_{V_{C,K}}$ of the $C-$extremal plurisubharmonic function $V_{C,K}$ for $C \subset (\mathbb{R}^+)^2$ a triangle $T_{a,b}$ with vertices $(0,0), (b,0), (0,a)$. Finally, we show how the definition of $δ_C(K)$ can be extended to include many nonconvex bodies $C\subset \mathbb{R}^d$ for $d-$circled sets $K\subset \mathbb{C}^d$, and we prove an integral formula for $δ_C(K)$ which we use to compute a formula for the $C-$transfinite diameter of the Euclidean unit ball $\mathbb{B}\subset \mathbb{C}^2$.
