Equivariant free boundary minimal discs and annuli in ellipsoids
Mario B. Schulz
TL;DR
This paper introduces new nonplanar free boundary minimal discs and proves the existence of multiple symmetric free boundary minimal annuli in ellipsoids using equivariant variational methods.
Contribution
It presents novel constructions of free boundary minimal surfaces in ellipsoids and establishes the existence of multiple symmetric annuli, advancing understanding of minimal surface geometry.
Findings
Existence of nonplanar free boundary minimal discs in ellipsoids.
At least three distinct embedded free boundary minimal annuli with dihedral symmetry in each ellipsoid.
Application of equivariant variational methods to construct minimal surfaces.
Abstract
We employ equivariant variational methods to construct new examples of nonplanar free boundary minimal discs in ellipsoids. We also prove that every ellipsoid contains at least three distinct embedded free boundary minimal annuli with dihedral symmetry.
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Taxonomy
TopicsMathematics and Applications · Point processes and geometric inequalities · Advanced Differential Equations and Dynamical Systems