Time: 9h00, Wednesday, October 16, 2019,
Location: Room 507-508, Building A6, Institute of Mathematics
Abstract: In this talk, we discuss a so-called Hardy-Moser-Trudinger inequality which combines both the sharp Hardy inequality and the sharp Moser-Trudinger inequality in the unit ball. This inequality was previously proved by G. Wang and D. Ye in dimension two via the blow-up analysis method. In this talk, we provide an extension of this inequality to higher dimensions. The proof combines the rearrangement argument together with the method of transplantation of Green functions without using the blow-up analysis method. As a consequence, we obtain a sharp Moser-Trudinger type inequality in the hyperbolic space which was conjectured by G. Mancini, K. Sandeep and C. Tintarev.