Capillary $L_p$ dual Minkowski flow

Abstract

For $n\geq2$ and $θ\in(0,π/2)$, we study the long-time existence and asymptotic behavior of an even normalized capillary $L_p$ dual Minkowski flow in the Euclidean half-space $\overline{\mathbb{R}^{n+1}_+}$. When $pq\geq0$, the flow exists for all positive time and the evolving hypersurfaces converge smoothly along a sequence of times tending to infinity to a stationary solution of the normalized problem. If $p\neq q$, a dilation of the limit solves the unnormalized problem.