Drums Love Hermann Weyl

Lotfi Hermi, University of Arizona

Abstract: There is analogy between inequalities involving the base frequency of a fixed membrane and those involving the (scaled) volume for a free membrane. We exploit this observation to prove two new bounds of Weyl-type growth for the higher pure tones of a drum. The new bounds complement those of Li-Yau, and extend earlier results of Ashbaugh-Benguria and Chiti.