By Sam Edwards
For a rank one geometrically finite locally symmetric space Γ\X, the bottom of the $L^2$ spectrum of the Laplace operator is a simple eigenvalue corresponding to a positive eigenfunction if and only if the critical exponent of Γ is strictly greater than half the volume entropy of X. In particular, there exist infinite volume rank one locally symmetric spaces with square integrable positive Laplace eigenfunctions. In contrast, a higher-rank symmetric space Γ\X without rank one factors has a square integrable positive Laplace eigenfunction if and only Γ is a lattice. We will explain some aspects of the connection between square integrability of positive Laplace eigenfunctions and Patterson-Sullivan and Bowen-Margulis-Sullivan measures in the higher-rank setting. Based on joint work with Oh and Fraczyk-Lee-Oh.
By Jean-François Quint
By Jean-François Quint
By Pierre-Louis Blayac
By Jean-François Quint
By Pratyush Sarkar
By Sam Edwards
By Minju Lee
By Andrés Sambarino
By Minju Lee
By Giuseppe Martone
By Andrés Sambarino
By Leon Carvajales
By Juan Camilo Arosemena Serrato
By Pieter Spaas
By Chao Li
By Juan Camilo Arosemena Serrato
By Francesca Arici
By Shirly Geffen
By Amine Marrakchi
By Pieter Spaas
