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EQUILATERAL DIMENSION OF THE UPPER HALF SPACE WITH HYPERBOLIC TYPE METRIC
Keywords:
hyperbolic type metric, equilateral dimensionDOI:
https://doi.org/10.17654/0972087125012Abstract
Let $\mathbb{H}^n$ be the upper half space. Then we define the hyperbolic type metric as follows:
$$
d(x, y)=\log \left(1+c \frac{|x-y|}{\sqrt{x_n y_n}}\right),
$$
where $x=\left(x_1, x_2, \ldots, x_n\right), \quad y=\left(y_1, y_2, \ldots, y_n\right) \in \mathbb{H}^n$ and $c \geq 2$ on $\mathbb{H}^n$. In this paper, we calculate the equilateral dimension of this metric space and show that it is $n+1$.
Received: January 15, 2025
Accepted: March 10, 2025
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