Title: New monotonicity formulas for the Green function

Speaker: Jiewon Park(KAIST)

Abstract: Numerous monotonicity formulas involving the Green function have been discovered in recent years. They are important tools leading to new breakthroughs and novel proofs of significant theorems. In this talk we prove a new family of monotonicity formulas for the Green function on manifolds supporting a certain functional inequality, which we call Property (HG), as well as rigidity theorems in the case of equality. We also discuss explicit examples of manifolds which has Property (HG). Time permitting, we will also discuss a related forthcoming result on quantitative almost rigidity of such monotonicity formulas, which is joint work with Christine Breiner.