A sharp lower bound for the nodal volume of harmonic functions

Let $u$ be a non-zero real-valued harmonic function in $B_4\subset\mathbb{R}^n$ with $n\geq3$ and $u(0)=0$. We prove that $$\mathcal{H}^{n-1}\bigl(\{u(x)=0\}\cap B_2\bigr)\ge C_n\mathcal{N},$$ where $C_n$ is a positive constant depending only on $n$, and $\mathcal{N}$ is the doubling index defined b