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Mergelyan
approximation theorem for holomorphic Legendrian curves
Franc Forstnerič |
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Vol. 15 (2022), No. 4, 983–1010
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Abstract |
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We prove a Mergelyan-type approximation theorem for immersed holomorphic Legendrian curves in an arbitrary complex contact manifold . Explicitly, we show that if is a compact admissible set in a Riemann surface and is a -Legendrian immersion of class for some which is holomorphic in the interior of , then can be approximated in the topology by holomorphic Legendrian embeddings from open neighbourhoods of into . This has numerous applications, some of which are indicated in the paper. In particular, by using Bryant’s correspondence for the Penrose twistor map we show that a Mergelyan approximation theorem and the Calabi–Yau property hold for conformal superminimal surfaces in the -sphere . |
Keywords
complex contact manifold, Legendrian curve, Mergelyan
theorem, superminimal surface
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Mathematical Subject Classification 2010
Primary: 53D35, 32E30, 34D10
Secondary: 37J55, 53A10
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Milestones
Received: 14 January 2020
Revised: 9 July 2020
Accepted: 11 December 2020
Published: 3 September 2022
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Authors |
| Franc Forstnerič | |
| Faculty of Mathematics and
Physics University of Ljubljana Ljubljana Slovenia |
Institute of Mathematics, Physics
and Mechanics Ljubljana Slovenia |
