Abschätzungen für das Spektrum von ${\Delta }_p$ auf Räumen konstanter Krümmung

Abstract

We present estimations for the first eigenvalue of ${\Delta }_p$ on spaces $M$ of constant curvature in terms of vol ($M$), $d_M$ and the radius of the greatest geodesic ball contained in $M$. The applied method in an essential way uses the zeros of spherical functions.