BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jeong Hyeong Park (Sungkyunkwan University) DTSTART:20220309T120000Z DTEND:20220309T130000Z DTSTAMP:20260423T052924Z UID:VSGS/44 DESCRIPTION:Title: Re cent progress on harmonic manifolds\nby Jeong Hyeong Park (Sungkyunkwa n University) as part of Virtual seminar on geometry with symmetries\n\n\n Abstract\nA Riemannian manifold (M\, g) is harmonic if there exists a nonc onstant radial harmonic function in a punctured neighborhood for any point \, or equivalently if a volume density function centered at a point depend s only on the distance from the center. There are many other characterizat ions of harmonic spaces. For example\, it is known that (M\, g) is a harmo nic space if and only if every sufficiently small geodesic sphere has cons tant mean curvature. Szabo proved that in a harmonic space\, the volume of the intersection of two geodesic balls of small radii depends only on the radii and the distance between the centers.\nIn this talk\, we classify h armonic spaces by using the asymptotic series of the density function and eigenvalues of the Jacobi operator\, and characterize harmonic spaces in t erms of the radial eigenspaces of the Laplacian. We discuss our recent pro gress on harmonic spaces. (This is joint work with P. Gilkey)\n LOCATION:https://researchseminars.org/talk/VSGS/44/ END:VEVENT END:VCALENDAR