论文标题
部分可观测时空混沌系统的无模型预测
Minimizing properties of networks via global and local calibrations
论文作者
论文摘要
在本说明中，我们证明，最小的网络可最大程度地减少长度功能的属性。大概是一个最小的网络，是$ \ mathbb {r}^2 $的子集，由在三个连接处加入的直段组成，形成等于$ \tfrac23π$的角度。特别地，这样的对象只是长度功能a的关键点。 我们表明，最小网络$γ_*$：i）最大程度地减少具有$γ_*$，ii的合适组中系数的电流的质量，识别$γ_*$的分区的接口，以解决具有相同边界痕迹的分区之间的最小分区问题。 讨论了这种结果的后果和清晰度。根据与最小网络相关的（全局或本地）校准的展览，证明将相当简单，直接的参数减少。
In this note we prove that minimal networks enjoy minimizing properties for the length functional. A minimal network is, roughly speaking, a subset of $\mathbb{R}^2$ composed of straight segments joining at triple junctions forming angles equal to $\tfrac23 π$; in particular such objects are just critical points of the length functional a priori. We show that a minimal network $Γ_*$: i) minimizes mass among currents with coefficients in a suitable group having the same boundary of $Γ_*$, ii) identifies the interfaces of a partition of a neighborhood of $Γ_*$ solving the minimal partition problem among partitions with same boundary traces. Consequences and sharpness of such results are discussed. The proofs reduce to rather simple and direct arguments based on the exhibition of (global or local) calibrations associated to the minimal network.
