Orlicz–Minkowski flows

Abstract

AbstractWe 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 $$L_p$$ L p version is the even $$L_p$$ L p -Minkowski problem for $$p>-n-1$$ 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 $$L_p$$ L p versions are the even $$L_p$$ L p -Minkowski problem for $$p>0$$ p > 0 and the $$L_p$$ L p -Minkowski problem for $$p>1$$ p > 1 . In the final section, we use a curvature flow with no global term to solve a class of $$L_p$$ L p -Christoffel–Minkowski type problems.