Jeong Hyeong Park, Sungkyunkwan University, Korea

Title: Harmonic manifolds

Abstract: A Riemannian manifold is harmonic if a volume density
function centered at a point depends only on the distance from the
center. In this talk, we focus on two questions:

1. To what extent does information about the volume density function
of a harmonic manifold determine its geometry?

2. To what extent the property of a manifold to be harmonic is inherited
by a submanifold? We characterize harmonic manifolds via density
functions and radial eigen functions and we also examine the totally
geodesic submanifolds of harmonic manifolds.