Warped product spaces: Gromov hyperbolicity and identification of the visual boundary

Josh Kline; Nageswari Shanmugalingam; Gareth Speight; Yi Wang

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arXiv · 2607.29685

Warped product spaces: Gromov hyperbolicity and identification of the visual boundary

Josh Kline·Nageswari Shanmugalingam·Gareth Speight·Yi Wang

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Abstract

In this paper, we consider warped product spaces $X\times_φY$, where $X$ is a complete geodesic Gromov hyperbolic space, $Y$ is a compact geodesic metric space, and the warping function $φ$ satisfies suitable exponential growth conditions. We prove that the warped product is Gromov hyperbolic and derive an explicit estimate for its hyperbolicity constant. We further establish a homeomorphism between its Gromov boundary and $\partial_GX\times Y$, with an explicit comparison formula for the visual metric on the Gromov boundary of $X\times_φY$ in terms of the visual metric $d_{\varepsilon, X}$ on $\partial_GX$ and $d_Y$ for suitable $\varepsilon>0$.

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BibTeX RIS

Josh Kline, Nageswari Shanmugalingam, Gareth Speight, Yi Wang. 2026-07-31. Warped product spaces: Gromov hyperbolicity and identification of the visual boundary. https://arxiv.org/abs/2607.29685

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