The $L_p$-dual Christoffel-Minkowski problem for the case $p\ge q$

Abstract

In this paper, we consider a class of Hessian equations associated to the $L_p$-dual Christoffel-Minkowski problem for the case $p\ge q$. By combining the tools of constant rank theorem, the a priori estimates and the continuity method, we obtain the existence and uniqueness for strictly spherical convex solutions to the $L_p$-dual Christoffel-Minkowski problem.