多个度量之和的Gromov双曲性
Gromov hyperbolicity of sums of metrics
曹杰军 1张孝惠1
作者信息
- 1. 浙江理工大学理学院,杭州 310018
- 折叠
摘要
为了将度量空间的Gromov双曲性由单个度量推广到多个度量,研究了对数型度量的性质,讨论了多个近似超度量之和的Gromov双曲性,并给出了由两个Gromov双曲度量之和构造一个新的Gromov双曲度量的例子.在Ptolemy空间中,由距离函数的上确界定义了一个含参数的度量,并证明了不同参数的度量之和的Gromov双曲性.特别地,借助类对数型度量变换的性质,推广了 Gromov双曲空间的一般构造法.
Abstract
In order to generalize the Gromov hyperbolicity of metric spaces from a single metric to multiple metrics,we discuss the Gromov hyperbolicity of sums of approximate ultrametrics by showing certain properties of logarithmic metrics.As an example,we construct a new Gromov hyperbolic space by the sum of two Gromov hyperbolic metrics.In a Ptolemy space,we define a metric with a parameter by the supremum of a distance function and further prove the Gromov hyperbolicity of sums of these metrics with different parameters.Specially,we extend a general construction of Gromov hyperbolic metric based on properties of logarithm-like metric transforms.
关键词
Gromov双曲性/近似超度量/度量变换/度量之和Key words
Gromov hyperbolicity/approximate ultrametric/metric transform/sum of metrics引用本文复制引用
基金项目
国家自然科学基金项目(11771400)
浙江省自然科学基金项目(LY22A010004)
出版年
2024
NETL
NSTL
万方数据