Holomorphic mappings of once-holed tori, II
In our previous work , 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.
- J. Kahn, K. M. Pilgrim and D. P. Thurston, Conformal surface embeddings and extremal length, preprint, arXiv:1507.05294[math.CV].Google Scholar
- M. Masumoto, On critical extremal length for the existence of holomorphic mappings of once-holed tori, J. Inequal. Appl. 2013 (2013), article no. 282.Google Scholar