Abstract: Consider a Schrödinger operator defined in the Euclidean space. In their celebrated 1976 paper, Lieb and Thirring proved an upper bound on the Riesz means of such an operator involving an integral of a power of the potential. Finding optimal constants in special cases of this inequality has been an active area of research for the past decades.
In this talk we prove that these Lieb—Thirring inequalities in Euclidean space easily translate to corresponding inequalities for Schrödinger operators in Hyperbolic space and that the optimal constant can be retained.