The Existence of Solution to the Even Orlicz Chord Minkowski Problem

Chord measures are newly discovered translation-invariant geometric measures of convex bodies in Rn by Lutwak-Xi-Yang-Zhang (Communications on Pure and Applied Mathematics, 2024), which is an extension of the surface area measure. The Minkowski problems for chord measures was considered by Lutwak-Xi-Yang-Zhang. In this paper, we use variational method to solve the even Orlicz chord Minkowski problem. The obtained results are an extension of the even Orlicz Minkowski problem from Haberl-Lutwak-Yang-Zhang (Advances in Mathematics, 2010 ).