This paper concerns the $L_p$ dual Minkowski problem, which amounts to solving a class of Monge-Ampère type equations on the sphere. Our main purpose is to show the existence of solutions to the problem for all $p>0$ via the study of related parabolic flows. We also discuss the problem when $p<0$. The regularity and uniqueness of the solutions are also studied.

中文翻译：

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的大号_p双闵可夫斯基和问题相关的抛物流动

本文涉及 ${升}_{磷}$对偶 Minkowski 问题，相当于求解球体上的一类 Monge-Ampère 型方程。我们的主要目的是向所有人展示问题的解决方案$磷>0$通过对相关抛物线流动的研究。我们也讨论这个问题时$磷<0$. 还研究了解的规律性和唯一性。