论文标题
Orlicz-Minkowski流
Orlicz-Minkowski flows
论文作者
论文摘要
我们研究一类各向异性非均匀的高斯曲率流的长期存在和行为，这些曲率流动的固定溶液（如果存在）解决了常规的Orlicz-Minkowski问题。作为一个应用程序，我们为常规的Orlicz-Minkowski问题获得了新的和新的结果；相应的$ l_p $版本是$ p> -n-1 $的$ l_p $ -minkowski问题。此外，采用抛物线近似方法，我们为一般的Orlicz-Minkowski问题提供了新的证据。 $ l_p $版本是$ p> 0 $的$ l_p $ -minkowski问题，$ p $ -minkowski问题$ p> 1 $。在最后一节中，我们使用没有全局术语的曲率流来解决$ L_P $ -CHRISTOFFEL-MINKOWSKI类型问题的类别。
We study the long-time existence and behavior for a class of anisotropic non-homogeneous Gauss curvature flows whose stationary solutions, if exist, solve the regular Orlicz-Minkowski problems. As an application, we obtain old and new results for the regular even Orlicz-Minkowski problems; the corresponding $L_p$ version is the even $L_p$-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 $L_p$ versions are the even $L_p$-Minkowski problem for $p>0$ and the $L_p$-Minkowski problem for $p>1$. In the final section, we use a curvature flow with no global term to solve a class of $L_p$-Christoffel-Minkowski type problems.
