On the three ball theorem for solutions of the Helmholtz equation

Stine Marie Berge, Eugenia Malinnikova

Let $u_k$ be a solution of the Helmholtz equation with the wave number $k$, $\Delta u_k+k^2{u}_k=0$, on a small ball in either ${\mathbb{R}}^n$, ${\mathbb{S}}^n$, or ${\mathbb{H}}^n$. For a fix…