Isotopies of complete minimal surfaces of finite total curvatureAlarcón, Antonio (Avtor) Forstnerič, Franc (Avtor) Lárusson, Finnur (Avtor) Riemann surfacesminimal surfacealgebraic immersionsdirected immersionsalgebraically elliptic manifoldflexible manifoldOka manifoldLet $M$ 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 ${\mathbb C}^n \setminus \{0\}$.20262026-07-23 12:54:03Neznano31268UDK: 517.5ISSN pri članku: 0024-6107DOI: 10.1112/jlms.70640COBISS_ID: 285548547sl