Holomorphic Legendrian curves in convex domains

Svetina, Andrej (avtor)

We prove several results on approximation and interpolation of holomorphic Legendrian curves in convex domains in ${\mathbb C}^{2n+1}$, $n \ge 2$, with the standard contact structure. Namely, we show that such a curve, defined on a compact bordered Riemann surface $M$, whose image lies in the interior of a convex domain ${\mathcal D} \subset {\mathbb C}^{2n+1}$, may be approximated uniformly on compacts in the interior ${\rm Int} M$ by holomorphic Legendrian curves ${\rm Int} M \to {\mathcal D}$ such that the approximants are proper, complete, agree with the starting curve on a given finite set in ${\rm Int} M$ to a given finite order, and hit a specified diverging discrete set in the convex domain. We first show approximation of this kind on bounded strongly convex domains and then generalise it to arbitrary convex domains. As a consequence we show that any compact bordered Riemann surface properly embeds into a convex domain as a complete curve under a suitable geometric condition on the boundary of the codomain.

• Jezik: Angleški jezik
• Ključne besede: holomorphic Legendrian curve, convex domain, complete Legendrian embedding
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2025
• Št. strani: 32 str.
• Številčenje: Vol. 35, iss. 1, art. 37
• PID: 20.500.12556/RUL-175141
• UDK: 517.5
• ISSN pri članku: 1050-6926
• DOI: 10.1007/s12220-024-01872-7
• COBISS.SI-ID: 218411523
• Datum objave v RUL: 17.10.2025

Gradivo je del revije

• Naslov: The journal of geometric analysis
• Skrajšan naslov: J. geom. anal.
• Založnik: Springer Nature, Mathematica Josephina
• ISSN: 1050-6926
• COBISS.SI-ID: 30685696

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.

Projekti

• Financer: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
• Program financ.: Young researchers

• Financer: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
• Številka projekta: P1-0291
• Naslov: Analiza in geometrija