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.
Gromov hyperbolicityapproximate ultrametricmetric transformsum of metrics
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