经典的 Minkowski 问题是凸几何中一个最基本的问题，它要求确定球面上的给定 Borel 测度是某个凸体对应的表面积测度的充分必要条件。一般地，我们称预定凸体的某种几何测度的问题为 Minkowski 型问题；若给定 Borel 测度的密度函数是常值时，我们称该问题是迷向的。在本论文中，我们对欧氏空间和双曲空间中几类重要的迷向 Minkowski 型问题给出了一些唯一性和分类结果。欧氏空间中的 $L_p$ 对偶 Minkowski 问题由 Lutwak，Yang 和 Zhang 提出，统一了 $L_p$ Minkowski 问题和对偶 Minkowski 问题。首先，对于欧氏平面中的迷向 $L_p$ 对偶 Minkowski 问题，通过研究一类含参数 $(p,q,r)$ 的广义积分的渐近行为、对偶关系和单调性，我们得到了该问题解的完全分类。其次，对于 $(n+1)$ 维欧氏空间中的迷向 $L_p$ 对偶 Minkowski 问题，利用局部 Brunn-Minkowski 不等式，我们证明了在 $-n-1

The classical Minkowski problem is one of the most fundamental problems in convex geometry, which asks for the necessary and sufficient conditions for a given Borel measure on the sphere to be the surface area measure of some convex body. Generally, we refer to the problem of determining a convex body with a prescribed certain geometric measure as a Minkowski type problem; and if the density function of the given Borel measure is constant, we call it an isotropic problem. In this paper, we provide some uniqueness and classification results for several important isotropic Minkowski type problems in Euclidean space and hyperbolic space.The $L_p$ dual Minkowski problem in Euclidean space, introduced by Lutwak, Yang, and Zhang, unifies the $L_p$ Minkowski problem and the dual Minkowski problem. Firstly, for the isotropic $L_p$ dual Minkowski problem in Euclidean plane, by studying the asymptotic behavior, duality relationship, and monotonicity of a class of generalized integrals with parameters $(p, q, r)$, we obtain a complete classification of the solutions to this problem. Secondly, for the isotropic $L_p$ dual Minkowski problem in $(n+1)$-dimensional Euclidean space, using the local Brunn-Minkowski inequality, we prove the uniqueness of solutions when $-n-1