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Jul 6, 2021 at 16:24 comment added markvs I would suggest you rewrite the question making it more readable.
Jul 6, 2021 at 15:18 comment added M. Dus @MarkSapir About the fixed exponential divergence, I mean an exponential divergence not depending on the geodesic. To be more specific, I would hope to find an exponential divergence depending only on the distance from x to hyperplanes one the left and on the right, among the family of strongly separated hyperplanes.
Jul 6, 2021 at 15:16 comment added M. Dus @MarkSapir Well, about infimal length first : I didn't write a precise definition of divergence on purpose, because there are several (non-equivalent ones) in litterature. Usually, it is defined as the minimum length of a path from $\gamma(-r)$ to $\gamma(r)$ avoiding the ball around $x$ (assuming here that $\gamma(0)=x$). Anyway, whatever precise definition you take, you always a super-linear divergence for a geodesic that crosses an infinite number of strongly separated hyperplanes.
Dec 8, 2020 at 0:19 comment added markvs What is "fixed exponential divergence" or "infimal length"?
Dec 3, 2020 at 9:42 history edited YCor CC BY-SA 4.0
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Dec 3, 2020 at 9:28 history asked M. Dus CC BY-SA 4.0