几何分析系列报告之02【李向东】

摘要: In his 1781 M´emoire sur la th´eorie des d´eblais et des remblais, Gaspard Monge raised the optimal transport problem and studied this problem using the ideas from differential geometry of curves and surfaces. He derived the differential equation of the optimal transport map between two regions in the plane and the three dimensional space, which includes the first Monge-Amp`ere equation in the literature. In this talk, I will explain Monge’s m´emoire in details and extend his ideas to hypersurfaces in Euclidean spaces.