Gauss curvature flow to the Lₚ-Gaussian chord Minkowski problem

Recently, Huang and Qin HY01 introduced Gaussian chord measure and Lₚ-Gaussian chord measure by variational methods. Meanwhile, they posed Gaussian chord Minkowski problem and used variational methods to obtain an origin-symmetric normalized measure solution for the Gaussian chord Minkowski problem. Motivated by the forgoing works of Lₚ-Gaussian chord measure, we can not only propose the Lₚ-Gaussian chord Minkowski problem, but also obtain its smooth solutions. Specially, we provide a smooth even solution for p=0. In this paper, we obtain the existence of smooth even solutions to the Lₚ-Gaussian chord Minkowski problem with p 0 and q>2 by method of a Gauss curvature flow.