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Embedded complex curves in the affine plane
ID
Alarcón, Antonio
(
Author
),
ID
Forstnerič, Franc
(
Author
)
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https://link.springer.com/article/10.1007/s10231-023-01418-8
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Abstract
This paper brings several contributions to the classical Forster-Bell-Narasimhan conjecture and the Yang problem concerning the existence of proper and almost proper (hence complete) injective holomorphic immersions of open Riemann surfaces in the affine plane ${\mathbb C}^2$ satisfying interpolation and hitting conditions. We also show that in every compact Riemann surface there is a Cantor set whose complement admits a proper holomorphic embedding in ${\mathbb C}^2$. The focal point is a lemma saying the following. Given a compact bordered Riemann surface, $M$, a closed discrete subset $E$ of its interior ${\mathring M}=M\setminus bM$, a compact subset $K\subset {\mathring M}\setminus E$ without holes in $\mathring M$, and a ${\cal C}^1$ embedding $f: M\hookrightarrow \mathbb C^2$ which is holomorphic in $\mathring M$, we can approximate $f$ uniformly on $K$ by a holomorphic embedding $F: bM\hookrightarrow {\mathbb C}^2$ which maps $E\cup bM$ out of a given ball and satisfies some interpolation conditions.
Language:
English
Keywords:
Riemann surfaces
,
complex curves
,
complete holomorphic embedding
Work type:
Article
Typology:
1.01 - Original Scientific Article
Organization:
FMF - Faculty of Mathematics and Physics
Publication version:
Version of Record
Publication date:
01.08.2024
Year:
2024
Number of pages:
Str. 1673-1701
Numbering:
Vol. 203, iss. 4
PID:
20.500.12556/RUL-159621
UDC:
517.5
ISSN on article:
0373-3114
DOI:
10.1007/s10231-023-01418-8
COBISS.SI-ID:
182950147
Publication date in RUL:
15.07.2024
Views:
100
Downloads:
5
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Record is a part of a journal
Title:
Annali di matematica pura ed applicata
Shortened title:
Ann. mat. pura appl.
Publisher:
Springer
ISSN:
0373-3114
COBISS.SI-ID:
24962816
Licences
License:
CC BY 4.0, Creative Commons Attribution 4.0 International
Link:
http://creativecommons.org/licenses/by/4.0/
Description:
This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.
Secondary language
Language:
Slovenian
Keywords:
Riemannove ploskve
,
kompleksne krivulje
,
kompletna holomorfna vložitev
Projects
Funder:
Other - Other funder or multiple funders
Funding programme:
Spain, State Research Agency (AEI)
Project number:
PID2020-117868GB-I00
Funder:
Other - Other funder or multiple funders
Funding programme:
“Maria de Maeztu” Excellence Unit IMAG
Project number:
CEX2020-001105-M
Funder:
Other - Other funder or multiple funders
Funding programme:
Junta de Andalucía
Project number:
P18-FR-4049
Funder:
EC - European Commission
Project number:
101053085
Name:
Holomorphic Partial Differential Relations
Acronym:
HPDR
Funder:
ARIS - Slovenian Research and Innovation Agency
Project number:
P1-0291
Name:
Analiza in geometrija
Funder:
ARIS - Slovenian Research and Innovation Agency
Project number:
J1-3005
Name:
Kompleksna in geometrijska analiza
Funder:
ARIS - Slovenian Research and Innovation Agency
Project number:
N1-0237
Name:
Holomorfne parcialne diferencialne relacije
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