| Title: | Isotopies of complete minimal surfaces of finite total curvature |
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| Authors: | ID Alarcón, Antonio (Author)
ID Forstnerič, Franc (Author)
ID Lárusson, Finnur (Author) |
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| Files: |  PDF - Presentation file, download (539,47 KB)
MD5: DAE32956B18714D4846ACCB20363354A
 URL - Source URL, visit https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.70640
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | 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 ${\mathbb C}^n \setminus \{0\}$. |
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| Keywords: | Riemann surfaces, minimal surface, algebraic immersions, directed immersions, algebraically elliptic manifold, flexible manifold, Oka manifold |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.07.2026 |
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| Year of publishing: | 2026 |
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| Number of pages: | 29 str. |
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| Numbering: | Vol. 114, iss. 1 |
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| PID: | 20.500.12556/DiRROS-31268  |
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| UDC: | 517.5 |
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| ISSN on article: | 0024-6107 |
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| DOI: | 10.1112/jlms.70640 |
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| COBISS.SI-ID: | 285548547 |
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| Publication date in DiRROS: | 23.07.2026 |
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| Views: | 182 |
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| Downloads: | 162 |
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