Capillary $L_p$-Christoffel-Minkowski problem

TL;DR

This paper addresses the capillary $L_p$-Christoffel-Minkowski problem in the half-space for a specific range of p, providing existence results for even hypersurfaces and introducing key non-collapsing estimates.

Contribution

It extends previous existence results for the capillary Christoffel-Minkowski problem by solving it in the half-space for 1<p<k+1 with new non-collapsing estimates.

Findings

Established existence of solutions for even hypersurfaces in the specified range

Developed a non-collapsing estimate for height and support function

Extended prior results to a broader class of hypersurfaces

Abstract

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}.