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We study the long-time existence and behavior for a class of anisotropic non-homogeneous Gauss curvature flows whose stationary solutions, if they exist, solve the regular Orlicz–Minkowski problems. As an application, we obtain old and new existence results for the regular even Orlicz–Minkowski problems; the corresponding Lp version is the even Lp-Minkowski problem for p> - n- 1. Moreover, employing a parabolic approximation method, we give new proofs of some of the existence results for the general Orlicz–Minkowski problems; the Lp versions are the even Lp-Minkowski problem for p> 0 and the Lp-Minkowski problem for p> 1. In the final section, we use a curvature flow with no global term to solve a class of Lp-Christoffel–Minkowski type problems.
|Number of pages||25|
|Journal||Calculus of Variations and Partial Differential Equations|
|Publication status||Published - Feb 2021|