Closeness of DN maps between non-homeomorphic surfaces implies that the higher-genus surface's Schottky double develops arbitrarily short closed geodesics.
Zapiski Nauchnykh Seminarov POMI, 506, 57–66 (2021)
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On non-homeomorphic surfaces with close DN maps
Closeness of DN maps between non-homeomorphic surfaces implies that the higher-genus surface's Schottky double develops arbitrarily short closed geodesics.