Chung-Jun Tsai

Stability and Area-Minimizing Property of Higher-Dimensional Helicoids

For each integer $k\geq 1$, we study the $(k+1)$-dimensional helicoid $H_k\subset\mathbb{R}^{2k+1}$ parametrized by \[ (u_1,\ldots,u_k,s) \longmapsto \bigl(u_1e^{is},\ldots,u_ke^{is},s\bigr) \in \mathbb{C}^k\times\mathbb{R}\cong \mathbb{R}^{2k+1}. \] These helicoids form a basic and distinguished family of complete, pr...