The Minkowski problem in the sphere (Q6633908)

The authors use the min-max principle and the Gauss curvature flow to prove that there are at least two solutions to the famous Minkowski problem in the sphere. The min-max principle is a powerful tool in geometric analysis that generally uses the concept of minimizing or maximizing a functional over a space of geometric objects in order to prove the existence of critical points (solutions) to a given problem. The paper is written in an approachable manner, and is suitable to a large audience of readers, including early career mathematicians, postdoctoral researchers and graduate students.