10 papers analyzed
These studies suggest that Willmore rigidity involves the convergence of Willmore flow to a round sphere under certain conditions, the classification and regularity of Willmore surfaces, and the application of Willmore functional in various geometric and physical contexts.
Willmore rigidity is a concept in differential geometry and mathematical physics that deals with the properties and behavior of surfaces that minimize the Willmore energy, which is the integral of the squared mean curvature. This topic has applications in various fields, including the study of minimal surfaces, string theory, and the analysis of fluid interfaces.
Constrained Willmore Surfaces:
Willmore Flow and Stability:
Classical Dynamics and Willmore Functional:
Willmore Spheres in Riemannian Manifolds:
Equivariant Willmore Surfaces:
Rigidity and Non-Rigidity Results:
Analysis of Willmore Surfaces:
Static Interface Profiles:
The study of Willmore rigidity encompasses various aspects, from the characterization and optimization of constrained Willmore surfaces to the analysis of their stability and dynamics. Key findings include the convergence of Willmore flow to round spheres under small initial energy, the classification of equivariant Willmore surfaces, and the establishment of rigidity and non-rigidity results. These insights contribute to a deeper understanding of the geometric and physical properties of surfaces governed by the Willmore functional.
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