Capillary curvature images

Abstract

In this paper, we solve the even capillary $L_p$-Minkowski problem for the range $-n<p<1$ and $\hat{I}¸\in (0,\frac{\ddot{I}}{€}2)$. Our approach is based on an iterative scheme that builds on the solution to the capillary Minkowski problem (i.e., the case $p=1$) and leverages the monotonicity of a class of functionals under a family of capillary curvature image operators. These operators are constructed so that their fixed points, whenever they exist, correspond precisely to solutions of the capillary $L_p$-Minkowski problem.