Sets with small angles in self-contracted curves
Sets with small angles in self-contracted curves
复制标题
自收缩曲线中具有小角度的集合
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
V. Zolotov
中科院分区：
文献类型：
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作者：
V. Zolotov
研究了具有有界粗糙角的度量空间。E. Le Donne，T. Rajala和E. Walsberg含蓄地使用这个概念来证明无限的雪花不能等距嵌入到有限维的Banach空间。
我们证明了有界不可求长自收缩曲线包含有界粗糙角的度量子空间。它给出了一类度量空间中有界自收缩曲线的可求直性，这类度量空间包括可逆的$C^{\infty}$-Finsler流形，具有局部可扩测地线的局部紧$CAT（k）$-空间和具有局部可扩测地线的局部紧Busemann空间.
我们还将无限雪花不可嵌入的结果推广到这类空间。
We study metric spaces with bounded rough angles. E. Le Donne, T. Rajala and E. Walsberg implicitly used this notion to show that infinite snowflakes can not be isometrically embedded into finite dimensional Banach spaces.
We show that bounded non-rectifiable self-contracted curves contain metric subspaces with bounded rough angles. Which provides rectifiability of bounded self-contracted curves in a wide class of metric spaces including reversible $C^{\infty}$-Finsler manifolds, locally compact $CAT(k)$-spaces with locally extendable geodesics and locally compact Busemann spaces with locally extendable geodesics.
We also extend the result on non embeddability of infinite snowflakes to this class of spaces.