Inverse mean value property of solutions to the modified Helmholtz equation
Nikolay V. Kuznetsov · arXiv (Cornell University) · 2021
A theorem characterizing analytically balls in the Euclidean space $\RR^m$ is proved. For this purpose positive solutions of the modified Helmholtz equation are used instead of harmonic functions applied in previous results. The obtained Kuran type theorem is based on the volume mean value property of solutions to this equation.