A sharp lower bound for the nodal volume of harmonic functions

Zhehui Wang

Let $u$ be a non-zero real-valued harmonic function in $B_4\subset {\mathbb{R}}^n$ with $n\ge 3$ and $u(0)=0$. We prove that $$\mathcal{H}^{n-1}\bigl(\{u(x)=0\}\cap B_2\bigr)\ge C_n\m…