20.500.12556/DiRROS-31268 Isotopies of complete minimal surfaces of finite total curvature Let $M$ be a Riemann surface biholomorphic to an affine algebraic curve. We show that the inclusion of the space $\Re {\mathrm {NC}}_*(M,{\mathbb C}^n)$ of real parts of nonflat proper algebraic null immersions $M\to{\mathbb C}^n$, $n\ge 3$, into the space ${\mathrm {CMI}}_*(M,{\mathbb R}^n)$ of complete nonflat conformal minimal immersions $M\to{\mathbb R}^n$ of finite total curvature is a weak homotopy equivalence. We also show that the $(1,0)$-differential $\partial$, mapping ${\mathrm {CMI}}_*(M,{\mathbb R}^n)$ or $\Re{\mathrm {NC}}_*(M,{\mathbb C}^n)$ to the space ${\mathcal A}^1(M, {\mathbf A})$ of algebraic $1$-forms on $M$ with values in the punctured null quadric $\mathbf {A}\subset {\mathbb C}^n\setminus \{0\}$, is a weak homotopy equivalence. Analogous results are obtained for proper algebraic immersions $M\to{\mathbb C}^n$, $n\ge 2$, directed by a flexible or algebraically elliptic punctured cone in ${\mathbb C}^n \setminus \{0\}$. Riemann surfaces minimal surface algebraic immersions directed immersions algebraically elliptic manifold flexible manifold Oka manifold Riemannove ploskve minimalne ploskve algebraične imerzije usmerjene imerzije algebraično eliptična mnogoterost fleksibilna mnogoterost mnogoterost Oka true false true Angleški jezik Slovenski jezik Neznano 2026-07-23 12:54:03 2026-07-23 12:54:03 2026-07-24 03:52:04 0000-00-00 00:00:00 2026 0 0 29 str. iss. 1 Vol. 114 Jul. 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-07-01 517.5 0024-6107 10.1112/jlms.70640 285548547 Journal_of_London_Math_Soc_-_2026_-_Alarcón_-_Isotopies_of_complete_minimal_surfaces_of_finite_total_curvature.pdf Journal_of_London_Math_Soc_-_2026_-_Alarcón_-_Isotopies_of_complete_minimal_surfaces_of_finite_total_curvature.pdf 1 DAE32956B18714D4846ACCB20363354A 796691eb44e5b6b3e6915991c29f939e3e5d0025d37eeaee32bf94382c4483ba 6984df9c-8685-11f1-812a-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=48291 https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.70640 1 d3786fe4-8684-11f1-812a-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=48288 Inštitut za matematiko, fiziko in mehaniko 0 0 0