20.500.12556/RUL-175141 Holomorphic Legendrian curves in convex domains 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. holomorphic Legendrian curve convex domain complete Legendrian embedding true false true Angleški jezik Ni določen Članek v reviji 2025-10-17 14:40:17 2025-10-17 14:40:20 2025-12-06 04:05:59 0000-00-00 00:00:00 2025 0 0 32 str. iss. 1, art. 37 Vol. 35 Jan. 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.5 1050-6926 10.1007/s12220-024-01872-7 218411523 s12220-024-01872-7-1.pdf s12220-024-01872-7-1.pdf 1 9528EA3E649067B9F0721D3A290A6879 68b8bb0700fd45686a3ca37162c43ca0991c687a9188c17def4f7796d4553de3 7c609b1b-ab56-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=220437 https://link.springer.com/article/10.1007/s12220-024-01872-7 1 2d0aaaff-ab56-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=220436 Fakulteta za matematiko in fiziko 0 0 0