Zetian Yan
We prove that a stable $C^{1,1}$-to-edge properly embedded free boundary minimal hypersurface $Σ^3$ of a $4$-dimensional wedge domain $Ω^4_θ$ with angle $θ\in (0,π]$ is flat.
This paper contains 7 sections, 9 theorems, 75 equations.
Theorem 1.1
Suppose that $\left(\Sigma^3, \left\{\partial_3 \Sigma\right\}\right)\subset \left(\Omega^4, \left\{\partial_4 \Omega\right\}\right)$ is a stable $C^{1,1}$-to-edge properly embedded free boundary minimal hypersurface. There exists an explicit constant $C$ such that In particular, $\Sigma=\Omega\cap P$ where $P\in \mathbb{R}^4$ is a hyperplane.
