The Minkowski problem in differential geometry asked for necessary and sufficient conditions such that a positive smooth function on the sphere is the Gauss curvature of a convex hypersurface.  The Minkowski problem in differential geometry has been solved by Nirenberg, Pogorelov,  Cheng-Yau and others.We will introduce the Minkowski problems from the view point of integral and convex geometry that are inspired by Lutwak-Yang-Zhang in recent decades.

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