Month: June 2019

Let M be a closed Riemannian manifold and denote by X its universal covering space equipped with the pulled back Riemannian metric. There is an intimate relation between the Laplace operator on X and the fundamental group of M. One example of this is the result of Brooks from 1981: the fundamental group of M … Continue reading "Laplace operator and covering spaces"

Today I stumbled across a news article ( link ) written about someone (actually, Athanassios Fokas – a known mathematician) having announced progress on the Lindelöf hypothesis ( wikipedia ). The Lindelöf hypothesis is related to the Riemannian hypothesis and actually also follows from it – progress on the Lindelöf hypothesis would also mean progress … Continue reading "Lindelöf hypothesis"