Hartogs-Osgood theorem for separately harmonic functions

Let $h$ be a separately harmonic function on an open neighborhood of a $(m-1)$-dimensional compact submanifold $\Sigma$ in R$^m$ with $m\geq 2$. We show that $h$ can be extended to a separately harmonic function on the bounded component of R$^m-\Sigma$.

Hali tarjima qilinmagan