The Calabi–Yau problem for minimal surfaces with Cantor ends
Franc Forstnerič
University of Ljubljana, Slovenia
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Abstract
We show that every connected compact or bordered Riemann surface contains a Cantor set whose complement admits a complete conformal minimal immersion in with bounded image. The analogous result holds for holomorphic immersions into any complex manifold of dimension at least 2, for holomorphic null immersions into with , for holomorphic Legendrian immersions into an arbitrary complex contact manifold, and for superminimal immersions into any selfdual or anti-self-dual Einstein four-manifold.
Cite this article
Franc Forstnerič, The Calabi–Yau problem for minimal surfaces with Cantor ends. Rev. Mat. Iberoam. 39 (2023), no. 6, pp. 2067–2077
DOI 10.4171/RMI/1365