Embedded complex curves in the affine plane

Alarcón, Antonio (avtor), Forstnerič, Franc (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: Riemann surfaces, complex curves, complete holomorphic embedding
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Različica publikacije: Objavljena publikacija
• Datum objave: 01.08.2024
• Leto izida: 2024
• Št. strani: Str. 1673-1701
• Številčenje: Vol. 203, iss. 4
• PID: 20.500.12556/RUL-159621
• UDK: 517.5
• ISSN pri članku: 0373-3114
• DOI: 10.1007/s10231-023-01418-8
• COBISS.SI-ID: 182950147
• Datum objave v RUL: 15.07.2024

Gradivo je del revije

• Naslov: Annali di matematica pura ed applicata
• Skrajšan naslov: Ann. mat. pura appl.
• Založnik: Springer
• ISSN: 0373-3114
• COBISS.SI-ID: 24962816

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: Riemannove ploskve, kompleksne krivulje, kompletna holomorfna vložitev