Isotopies of complete minimal surfaces of finite total curvature
Abstract
Abstract Let be a Riemann surface biholomorphic to an affine algebraic curve. We show that the inclusion of the space of real parts of nonflat proper algebraic null immersions , , into the space of complete nonflat conformal minimal immersions of finite total curvature is a weak homotopy equivalence. We also show that the (1,0)‐differential , mapping or to the space of algebraic 1‐forms on with values in the punctured null quadric , is a weak homotopy equivalence. Analogous results are obtained for proper algebraic immersions , , directed by a flexible or algebraically elliptic punctured cone in .
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Geometry and complex manifolds
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- Journal of the London Mathematical Society
- Volume
- 114
- Issue
- 1
- Publication date
- 1 July 2026
- Language
- EN