20.500.12556/DiRROS-18392 Minimal surfaces with symmetries Minimalne ploskve s simetrijami 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 Neznano 2024-03-13 10:22:37 2024-03-13 10:22:38 2024-03-14 03:34:23 0000-00-00 00:00:00 2024 0 0 32 str. iss. 3, [article no.] e12590 Vol. 128 Mar. 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2024-03-01 517.5 0024-6115 10.1112/plms.12590 188644867 https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/plms.12590 1 3cc85446-e11b-11ee-9dd4-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=25037 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 DDCD746711142D30954B69AEDC137F4C 632b592a55e4d8e55027c254443b956423c122aaf94076a1e8ac86c0e0f54264 cd698499-e11b-11ee-9dd4-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=25038 Inštitut za matematiko, fiziko in mehaniko 0 0 0