Title: Parametrizations of Solutions to the Yamabe Equation with Isolated Singularities

Speaker: HAN Qing (Notre Dame University)

Time: 12th, May, 2025 (16:00-17:00)

Place: Room 1418, Managemet Building

Abstract: In this series of lectures, we study parametrizations of solutions to the Yamabe equation with nonremovable isolated singularities by harmonic functions, or more precisely, by sequences of spherical harmonics. There is a one-to-one correspondence between the collection of the solutions to the Yamabe equation with nonremovable isolated singularities and the collection of the sequences of spherical harmonics through formal infinite series determined by the sequences of spherical harmonics. We prove that these formal infinite series yield actual solutions to the Yamabe equation with a nonremovable isolated singularity. These solutions to the Yamabe equation have designated asymptotic behaviors determined by the sequences of spherical harmonics.