20.500.12556/RUL-154999 Minimal surfaces with symmetries Let $G$ be a finite group acting on a connected open Riemann surface $X$ by holomorphic automorphisms and acting on a Euclidean space ${\mathbb R}^n$ $(n\ge 3)$ by orthogonal transformations. We identify a necessary and sufficient condition for the existence of a $G$-equivariant conformal minimal immersion $F:X\to{\mathbb R}^n$. We show in particular that such a map $F$ always exists if $G$ acts without fixed points on $X$. Furthermore, every finite group $G$ arises in this way for some open Riemann surface $X$ and $n=2|G|$. We obtain an analogous result for minimal surfaces having complete ends with finite total Gaussian curvature, and for discrete infinite groups acting on $X$ properly discontinuously and acting on ${\mathbb R}^n$ by rigid transformations. Riemann surfaces minimal surfaces G-equivariant conformal minimal immersion Riemannove ploskve minimalne ploskve G-ekvivariantna konformna minimalna imerzija true false true Angleški jezik Slovenski jezik Članek v reviji 2024-03-13 11:13:45 2024-03-13 11:13:48 2024-05-09 03:52:43 0000-00-00 00:00:00 2024 0 0 32 str. iss. 3, art. e12590 Vol. 128 Mar. 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.5 0024-6115 10.1112/plms.12590 188644867 Proceedings_of_London_Math_Soc_-_2024_-_Forstneric_-_Minimal_surfaces_with_symmetries.pdf Proceedings_of_London_Math_Soc_-_2024_-_Forstneric_-_Minimal_surfaces_with_symmetries.pdf 1 4BD4CB142969C5A104CC0782E076C91A 71e71026bd147cd97743d0fe3e7e76c42f79156c709c128c5457cc398e5f187c 7cbf010a-0d27-11ef-a389-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=183347 https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/plms.12590 1 5ff61f8b-e122-11ee-88aa-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=181700 Fakulteta za matematiko in fiziko 0 0 0