A flow approach to the Musielak-Orlicz-Gauss image problem

In this paper, the extended Musielak-Orlicz-Gauss image problem is studied. Such a aims to characterize measure $\widetilde{C}_{G,\Psi,\lambda}(\Omega,\cdot)$ of convex body $\Omega$ in $\mathbb{R}^{n+1}$ containing origin (but not necessary its interior). particular, we provide solutions based on study suitably designed parabolic flows, and by use approximation technique (for general measures). Our flows involve two Musielak-Orlicz functions hence contain many well-studied curvature related Minkowski type problems as special cases. results only generalize previously known Gauss problems, but also those unsolved