Capillary $L_p$ Minkowski Flows

We study the long-time existence and asymptotic behavior of a class of anisotropic capillary Gauss curvature flows. As an application, we provide a flow approach to the existence of smooth solutions to the capillary even $L_p$ Minkowski problem in the Euclidean half-space for all $p\in (-n-1,\mathrm{\infty })$ and capillary $L_p$ Minkowski problem for $p>n+1$.