| Title: | The Calabi-Yau problem for minimal surfaces with Cantor ends |
|---|
| Authors: | ID Forstnerič, Franc (Author) |
|---|
| Files: |  PDF - Presentation file, download (516,47 KB)
MD5: 0BAFE7232DED29B49FB74D3E58B0F5E6
 URL - Source URL, visit https://ems.press/journals/rmi/articles/6866102
|
|---|
| Language: | English |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
|
|---|
| 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 |
|---|
| Publication status: | Published |
|---|
| Publication version: | Version of Record |
|---|
| Publication date: | 01.01.2023 |
|---|
| Year of publishing: | 2023 |
|---|
| Number of pages: | str. 2067-2077 |
|---|
| Numbering: | Vol. 39, no. 6 |
|---|
| PID: | 20.500.12556/DiRROS-18630  |
|---|
| UDC: | 517.5 |
|---|
| ISSN on article: | 0213-2230 |
|---|
| DOI: | 10.4171/RMI/1365 |
|---|
| COBISS.SI-ID: | 176903939 |
|---|
| Note: |
|
|---|
| Publication date in DiRROS: | 08.04.2024 |
|---|
| Views: | 1051 |
|---|
| Downloads: | 514 |
|---|
| Metadata: |    |
|---|
|
:
|
Copy citation |
|---|
| | | | Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
