Abstract
In our previous work [13], for a given Riemann surface Y0 with marked handle, we investigated geometric properties of the set of marked once-holed tori X allowing holomorphic mappings of X into Y0. It turned out to be a closed domain with Lipschitz boundary. In the present paper we show that the boundary is not smooth. Also, we evaluate the critical extremal length for the existence of holomorphic mappings in terms of hyperbolic lengths.
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The author really appreciates the referee’s careful reading and invaluable comments.
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This research is supported in part by JSPS KAKENHI Grant Number 26400140.
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Masumoto, M. Holomorphic mappings of once-holed tori, II. JAMA 139, 597–612 (2019). https://doi.org/10.1007/s11854-019-0069-8
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DOI: https://doi.org/10.1007/s11854-019-0069-8