Kavli Affiliate: Feng Wang
| First 5 Authors: Feng Wang, Emmett L. Wyman, Yakun Xi, ,
| Summary:
We address a maximally structured case of the question, "Can you hear your
location on a manifold," posed in arXiv:2304.04659 for dimension $2$. In short,
we show that if a compact surface without boundary sounds the same at every
point, then the surface has a transitive action by the isometry group. In the
process, we show that you can hear your location on Klein bottles and that you
can hear the lengths and multiplicities of looping geodesics on compact
hyperbolic quotients.
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