论文标题
高斯曲率流到$ L_P $ -Gaussian Minkowski问题
Flow by Gauss curvature to the $L_p$-Gaussian Minkowski problem
论文作者
论文摘要
在本文中，我们研究了$ l_p $ -Gaussian Minkowski问题，该问题在高斯概率空间中的$ L_P $ -BRUNN-MINKOWSKI理论中出现。我们将Aleksandrov与Lagrange倍增器一起使用Aleksandrov的变异方法来证明对数Gauss Minkowski问题的存在。 We construct a suitable Gauss curvature flow of closed, convex hypersurfaces in the Euclidean space $\mathbb{R}^{n+1}$, and prove its long-time existence and converges smoothly to a smooth solution of the normalized $L_p$ Gaussian Minkowski problem in cases of $p>0$ and $-n-1<p\leq 0$ with even prescribed function respectively.在$ p \ geq n+1 $和$ 0 <p <n+1 $的情况下，我们还为$ l_p $ -Gaussian Minkowski问题提供了平滑类别的抛物线证明，分别具有规定的功能。
In this paper, we study the $L_p$-Gaussian Minkowski problem, which arises in the $L_p$-Brunn-Minkowski theory in Gaussian probability space. We use Aleksandrov's variational method with Lagrange multipliers to prove the existence of the logarithmic Gauss Minkowski problem. We construct a suitable Gauss curvature flow of closed, convex hypersurfaces in the Euclidean space $\mathbb{R}^{n+1}$, and prove its long-time existence and converges smoothly to a smooth solution of the normalized $L_p$ Gaussian Minkowski problem in cases of $p>0$ and $-n-1<p\leq 0$ with even prescribed function respectively. We also provide a parabolic proof in the smooth category to the $L_p$-Gaussian Minkowski problem in cases of $p\geq n+1$ and $0<p<n+1$ with even prescribed function, respectively.
