Short-time existence of the Möbius-invariant Willmore flow

DOI10.1007/S12220-017-9857-5zbMath1393.53062OpenAlexW2610514594MaRDI QIDQ1651363

Ruben Jakob

Publication date: 12 July 2018

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12220-017-9857-5

zbMATH Keywords

short-time existenceWillmore flowMöbius-invarianceparabolic Schauder theory

Mathematics Subject Classification ID

Heat and other parabolic equation methods for PDEs on manifolds (58J35) Applications of functional analysis to differential and integral equations (46N20) PDEs on manifolds (35R01) Initial value problems for higher-order parabolic systems (35K46)

Related Items (4)

A minimising movement scheme for the \(p\)-elastic energy of curves ⋮ The Willmore flow of Hopf-tori in the 3-sphere ⋮ Global existence and full convergence of the Möbius-invariant Willmore flow in the 3-sphere ⋮ Functional analytic properties and regularity of the Möbius-invariant Willmore flow in \(\mathbb{R}^n\)

Cites Work

• Deforming metrics in the direction of their Ricci tensors
• Conformal invariants for curves and surfaces in three dimensional space forms
• Schauder estimates by scaling
• Parabolic boundary value problems
• Three-manifolds with positive Ricci curvature
• Gradient flow for the Willmore functional
• On the inversive differential geometry of plane curves
• A note on quasilinear parabolic equations on manifolds
• An Invariant of Conformal Mappings
• Conformal Differential Geometry of a Subspace
• Analytic semigroups and optimal regularity in parabolic problems

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