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- Title
The Calabi-Yau problem for minimal surfaces with Cantor ends.
- Authors
Forstnerič, Franc
- Abstract
We show that every connected compact or bordered Riemann surface contains a Cantor set whose complement admits a complete conformal minimal immersion in R³ with bounded image. The analogous result holds for holomorphic immersions into any complex manifold of dimension at least 2, for holomorphic null immersions into Cn with n≥3, for holomorphic Legendrian immersions into an arbitrary complex contact manifold, and for super-minimal immersions into any self-dual or anti-self-dual Einstein four-manifold.
- Subjects
EINSTEIN, Albert, 1879-1955; MINIMAL surfaces; COMPLEX manifolds; CANTOR sets; EINSTEIN manifolds; RIEMANN surfaces
- Publication
Revista Mathematica Iberoamericana, 2023, Vol 39, Issue 6, p2067
- ISSN
0213-2230
- Publication type
Article
- DOI
10.4171/RMI/1365