A degenerate free boundary minimal annulus and non-uniqueness in spherical caps beyond the hemisphere
Year: 2026
Type: preprint
Abstract: Let $\{Σ_a\}$, $a\in(0,1/2)$, be de Oliveira's family of embedded free boundary minimal annuli of revolution in geodesic balls $B(R(a))\subset\mathbb{S}^3$, $R(a)>π/2$. We prove that $R$ is real-analytic, tends to $π/2$ at both ends, and therefore folds: it has an interior maximum $R_*>π/2$ and is not injective. Hence each $B(ρ)$ with $π/2<ρπ/2$. The exact identity $\dim K_0^{ev}(Σ_a)=\mathbf{1}_{\{R'=0\}}(a)$ detects the degeneration; it follows from the symmetry-free relation $\partial_ηφ_a-\operatorname{ct}_κ(r(a))φ_a=r'(a)A_a(η,η)$, a Robin defect identity, which requires of the ambient only that the barrier family be umbilic and which extends to capillary boundary conditions at constant contact angle.
Source: arXiv (Cornell University)
Author: Pigazzini, Alexander
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7171521626