标题： 射影联络与解析内容的极值区域 显示英文标题

标题： Projective connections and extremal domains for analytic content

摘要： 这则注释扩展了最近的证明\cite{ABKT}，该证明表明二维空间中解析内容的极值区域只能是圆盘和环形区域。 这一结果对理论物理的意外启示是，对于极值区域而言，解析内容是(multiplicative)伴随算子$T, T^{\dag}$的非对易性的度量，其中$T^{\dag} = \bar z$，因此也是量子变形参数（“普朗克常数”）的度量。 环形解（其中包括圆盘作为特殊情况）实际上是一族连续的解，对应于变形参数的所有可能正值，这与二维空间中的共形不变性禁止存在特殊长度尺度的物理要求一致。 显示英文摘要

摘要： This note expands on the recent proof \cite{ABKT} that the extremal domains for analytic content in two dimensions can only be disks and annuli. This result's unexpected implication for theoretical physics is that, for extremal domains, the analytic content is a measure of non-commutativity of the (multiplicative) adjoint operators $T, T^{\dag}$, where $T^{\dag} = \bar z$, and therefore of the quantum deformation parameter (``Planck's constant"). The annular solution (which includes the disk as a special case) is, in fact, a continuous family of solutions, corresponding to all possible positive values of the deformation parameter, consistent with the physical requirement that conformal invariance in two dimensions forbids the existence of a special length scale.