Helicoidal surfaces of prescribed mean curvature in \(\mathbb{R}^3\)

DOI10.1007/s00025-024-02283-4MaRDI QIDQ6626464

Aires Eduardo Menani Barbieri

Publication date: 28 October 2024

Published in: Results in Mathematics (Search for Journal in Brave)

zbMATH Keywords

prescribed mean curvaturehelicoidal surfaces

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Ordinary differential equations and systems on manifolds (34C40)

Cites Work

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• A Hopf theorem for non-constant mean curvature and a conjecture of A. D. Alexandrov
• The structure of complete embedded surfaces with constant mean curvature
• Helicoidal surfaces with constant mean curvature
• Differential geometry in the large. Seminar lectures New York University 1946 and Stanford University 1956. With a preface by S. S. Chern.
• Convex hypersurfaces of prescribed curvatures
• Helicoidal surfaces rotating/translating under the mean curvature flow
• Rotational hypersurfaces of prescribed mean curvature
• The global geometry of surfaces with prescribed mean curvature in ℝ³
• On the Local Behavior of Solutions of Non-Parabolic Partial Differential Equations

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