Approximation of holomorphic Legendrian curves with jet-interpolation

Svetina, Andrej (author)

We prove several interpolation results for holomorphic Legendrian curves lying in an odd dimensional complex Euclidean space with the standard contact structure. In particular, we show that an arbitrary countable set of points in $\mathbb{C}^{2n+1}$ lies on an injectively immersed isotropic surface with a prescribed complex structure. If the set has no accumulation points, the surface may be taken properly embedded. We also prove a Carleman-type theorem for holomorphic Legendrian curves with interpolation. Namely, a Legendrian curve, defined on a certain type of unbounded closed set in a given open Riemann surface $\mathcal{R}$, may be approximated in the $\mathcal{C}^0$-topology by an entire Legendrian curve with prescribed finite-order Taylor polynomials at a closed discrete set of points in $\mathcal{R}$. Under suitable conditions, the approximating map may be made into a proper embedding.

• Language: English
• Keywords: holomorphic Legendrian curve, Carleman approximation, Mergelyan approximation
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2024
• Number of pages: 25 str.
• Numbering: Vol. 531, iss. 2, pt. 1, art. 127839
• PID: 20.500.12556/RUL-153029
• UDC: 517.5
• ISSN on article: 0022-247X
• DOI: 10.1016/j.jmaa.2023.127839
• COBISS.SI-ID: 173063683
• Publication date in RUL: 14.12.2023

Record is a part of a journal

• Title: Journal of mathematical analysis and applications
• Shortened title: J. math. anal. appl.
• Publisher: Elsevier
• ISSN: 0022-247X
• COBISS.SI-ID: 3081231

Licences

• License: CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Description: The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.

Secondary language

• Language: Slovenian
• Keywords: holomorfne Legendrove krivulje, Carlemanova aproksimacija, Mergelyanova aproksimacija

Projects

• Funder: ARRS - Slovenian Research Agency
• Funding programme: Young researchers

• Funder: ARRS - Slovenian Research Agency
• Project number: P1-0291
• Name: Analiza in geometrija