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Approximation of holomorphic Legendrian curves with jet-interpolation
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Svetina, Andrej
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)
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https://www.sciencedirect.com/science/article/pii/S0022247X23008429
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Abstract
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
Views:
509
Downloads:
26
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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
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