Surfaces of constant mean curvature and Alexandrov’s moving plane method

Abstract: In this talk we will follow Alexandrov's proof of the fact that spheres are the only compact surfaces in Euclidean space with constant mean curvature. The proof combines some techniques from elliptic PDEs with elementary geometric arguments. The moving plane method has been an important technique for proving symmetry and rigidity results in many settings in which PDEs originate from geometry.