On the lower bound of the inner radius of nodal domains (Q2421231)

For a closed, real analytic Riemannian manifold \(\left(M,g\right)\), the inradius of a nodal domain \(\Omega_{\lambda}\subset M\) of a eigenvalue \(\lambda\) eigenfunction satisfies \(c_{1}\lambda^{-1}\leq\text{inrad}\left(\Omega_{\lambda}\right)\leq c_{2}\lambda^{-1/2}\) for some constants. This uses related work of Donnelly-Fefferman and improves a similar bound of Mangoubi on smooth manifolds.