Capillary $L_p$-Christoffel-Minkowski problem

We solve the capillary $L_p$-Christoffel–Minkowski problem in the half-space for $1<p<k+1$ in the class of even hypersurfaces. A crucial ingredient is a non-collapsing estimate that yields lower bounds for both the height and the capillary support function. Our result extends the capillary Christoffel–Minkowski existence result of \cite{HIS25}.