Long-Zhi Lin

Energy convexity and uniformity of the $H$-surface flow in $\mathbb{R}^{3}$ with Dirichlet boundary condition

We prove that the energy functional associated with surfaces of prescribed mean curvature in $\mathbb{R}^3$ exhibits a convexity property when restricted to maps from the unit $2$-disk having small Dirichlet energy and a fixed boundary value, provided that the $3$-form $H \cdot \text{vol}_{\mathbb{R}^3}$ has a primitiv...