We will first introduce the classical Minkowski problem, the classical two series of geometric measures, and related isoperimetric inequalities including the Aleksandrov-Fenchel inequality and Brunn-Minkowski inequalities. The connection of Minkowski problem and PDE will also be included. Then we will discuss the new developments of Minkowski problem including the Lp Minkowski problems, dual Minkowski problems, and Lp Aleksandrov problems. Finally, we will talk about the Gaussian Minkowski problem and related Gaussian isoperimetric inequalities, which is a joint work with Huang Yong and Zhao Yiming.

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