论文标题
一类各向异性逆高斯曲率流和双重orlicz minkowski类型问题
A class of anisotropic inverse Gauss curvature flows and dual Orlicz Minkowski type problem
论文作者
论文摘要
在本文中，我们研究了一类各向异性逆高斯曲率流的长期存在和渐近行为。通过各向异性流的固定溶液，我们为双重的Minkowski类型问题获得了一些新的存在结果，甚至可以从双重观点观点观察到$ L^p $ Dual Minkowski问题的$ L^p $ Dual Minkowski问题的双重orlicz Minkowski类型问题。相应的$ l^p $版本的结果是$ l^p $双minkowski问题，$ p> q $;甚至$ l^p $ Dual minkowski问题$ p> -1 $，或$ q <1 $，或$ p <0 <q $的一些范围，这些范围包含所有存在的平滑度量结果，直到现在，除了$ p = q $或$ q = q = n+1 $（$ l^p $ minkowski问题）。
In this paper, we study the long-time existence and asymptotic behavior for a class of anisotropic inverse Gauss curvature flows. By the stationary solutions of anisotropic flows, we obtain some new existence results for the dual Orlicz Minkowski type problem and even dual Orlicz Minkowski type problem for smooth measures, which is the most reasonable extension of the $L^p$ dual Minkowski problem from the dual point of view. The results of corresponding $L^p$ versions are $L^p$ dual Minkowski problem for $p>q$; and even $L^p$ dual Minkowski problem for $p>-1$, or $q<1$, or some ranges of $p<0<q$, which contain all existence results for smooth measures up to now except $p=q$ or $q=n+1$ ($L^p$ Minkowski problem).
