Symmetry of embedded genus 1 helicoids

DOI10.1215/00127094-1384791zbMath1228.53008arXiv1011.3769OpenAlexW2011144563MaRDI QIDQ635475

Christine Breiner, Jacob Bernstein

Publication date: 19 August 2011

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.3769

zbMATH Keywords

symmetriesgenus \(k\) helicoidsgenus 1 helicoids

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Jacobians, Prym varieties (14H40)

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Cites Work

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• Conformal structure of minimal surfaces with finite topology
• Genus-one helicoids from a variational point of view
• Existence of smooth embedded surfaces of prescribed genus that minimize parametric even elliptic functionals on 3-manifolds
• Helicoids with handles and Baker-Akhiezer spinors
• The singly periodic genus-one helicoid
• The geometry of periodic minimal surfaces
• Some uniqueness and nonexistence theorems for embedded minimal surfaces
• An embedded genus-one helicoid
• On embedded complete minimal surfaces of genus zero
• Embedded minimal ends of finite type
• A uniqueness theorem for the singly periodic genus-one helicoid

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