The Other Pure Seminar (TOPS): On the method of moving planes and the P-function method (1 of 2)

Speaker: Giorgio Poggesi

Title: On the method of moving planes and the P-function method

Abstract: The mini-course will begin by considering the celebrated symmetry theorems established by Alexandrov in 1958 and Serrin in 1971. The first, Alexandrov’s soap bubble theorem, deals with constant mean curvature hypersurfaces, whereas the second, Serrin’s symmetry result, concerns certain overdetermined problems for partial differential equations (PDEs).

The original proofs by Alexandrov and Serrin introduced and developed the renowned method of moving planes, which has since proven to be a powerful and flexible tool still widely used to establish various results in PDEs. An alternative proof of Serrin’s symmetry result was famously given in the same year by Weinberger, based on what is now known as the P-function method. This approach has also become a powerful and versatile tool, still widely used to establish various results in PDEs.

In this mini-course, we will review the main ideas behind these powerful methods and explore some of their recent applications.