Special Session 7: Recent developments on nonlinear geometric PDEs

New ancient solutions to the Yamabe flow on the sphere
Seunghyeok Kim
Hanyang University
Korea
Co-Author(s):    Haixia Chen, Monica Musso
Abstract:
The Yamabe flow is a geometric evolution equation that aims to improve the geometry of a manifold by deforming its metric toward one with constant scalar curvature. In this talk, I will introduce the historical background for the Yamabe flow and then discuss recent developments concerning ancient solutions, namely, solutions that exist for all negative times. In the latter part of the talk, I will present joint work with Dr. Haixia Chen (Hanyang University, Central China Normal University) and Prof. Monica Musso (University of Bath) on the existence of non-rotationally symmetric ancient solutions.