Constructing Entire Minimal Graphs by Evolving Planes (joint with Chung-Jun Tsai, Mao-Pei Tsui, and Mu-Tao Wang)
Published in , 2025
We introduce an evolving-plane ansatz for the explicit construction of entire minimal graphs of dimension \(n\) (\(n \ge 3\)) and codimension \(m\) (\(m \ge 2\)), for any odd integer \(n\). Under this ansatz, the minimal surface system reduces to the geodesic equation on the Grassmannian in affine coordinates. Geometrically, this equation governs how the slope of an \((n-1)\)-plane evolves as it sweeps out a minimal graph. This framework yields a rich family of explicit entire minimal graphs of odd dimension \(n\) and arbitrary codimension \(m\). For each such entire minimal graph, its conormal bundle gives rise to an entire special Lagrangian graph in \(\mathbb{C}^{n+m}\).