On the first eigenvalue of Liouville-type problems
arXiv:2306.10256 · doi:10.1090/proc/17167
Abstract
The aim of this note is to study the spectrum of a linearized Liouville-type problem, characterizing the case in which the first eigenvalue is zero. Interestingly enough, we obtain also point-wise information on the associated first eigenfunction. To this end, we refine the Alexandrov-Bol inequality suitable for our problem and characterize its equality case.
14 pages