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The Calabi-Yau problem for minimal surfaces with Cantor endsFranc Forstnerič, 2023, original scientific article
Abstract: We show that every connected compact or bordered Riemann surface contains a Cantor set whose complement admits a complete conformal minimal immersion in ${\mathbb R}^3$ with bounded image. The analogous result holds for holomorphic immersions into any complex manifold of dimension at least $2$, for holomorphic null immersions into ${\mathbb C}^n$ with $n \ge 3$, for holomorphic Legendrian immersions into an arbitrary complex contact manifold, and for superminimal immersions into any selfdual or anti-self-dual Einstein four-manifold.
Keywords: minimal surfaces, Calabi–Yau problem, null curve, Legendrian curve
Published in DiRROS: 08.04.2024; Views: 82; Downloads: 38
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