发表机构
Syracuse University（雪城大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明配备瓶颈匹配度量的绝对λ-利普希茨收缩核的Q次对称积为绝对(3Q-2)λ-利普希茨收缩核，解答了De Pauw关于Almgren Q值映射目标空间的问题，核心工具为度量星有界积模有限置换群的重构定理。
AI 中文摘要
我们证明，配备瓶颈匹配度量的绝对λ-利普希茨收缩核的Q次对称积，是绝对(3Q-2)λ-利普希茨收缩核。这回答了De Pauw关于Almgren Q值映射的目标空间的问题。主要工具是关于带有限多条射线的度量星的有界积在有限置换群模下的重构定理：这些商空间是绝对3-利普希茨收缩核，与群和坐标数无关。
英文摘要
We prove that the Qth symmetric product of an absolute $λ$-Lipschitz retract, equipped with the bottleneck matching metric, is an absolute $(3Q-2)λ$-Lipschitz retract. This answers a question of De Pauw about the target spaces of Almgren's Q-valued maps. The main tool is a reconstruction theorem for bounded products of metric stars with finitely many rays, modulo a finite permutation group: these quotients are absolute 3-Lipschitz retracts, independently of the group and the number of coordinates.
