CMSA Mathematical Physics Seminar: On eigenvalues and eigenfunctions of the clamped plate
Dan Mangoubi - Einstein Institute of Mathematics
A celebrated theorem of C.L. Siegel from 1929 shows that the multiplicity of eigenvalues for the Laplace eigenfunctions on the unit disk is at most two. We study the fourth order clamped plate problem, showing that the multiplicity of eigenvalues is uniformly bounded. Our method is based on new recursion formulas and Siegel--Shidlovskii theory. If time permits, we discuss possible applications also to nodal geometry. The talk is based on a joint work with Yuri Lvovsky.