Let M be a compact C^∞-smooth Riemannian manifold of dimension n, n≥3, and let
\varphi_λ=\Delta_M\varphi_λ+λ\varphi_λ=0 denote the Laplace eigenfunction on M …

We prove that, for an n-dimensional compact Riemannian manifold (M, g), the (n− 1)-
dimensional Hausdorff measure| Z λ| of the zero-set Z λ of an eigenfunction e λ of the …

Let Δ M be the Laplace operator on a compact n-dimensional Riemannian manifold without
boundary. We study the zero sets of its eigenfunctions u: Δ M u+ λu= 0. In dimension n= 2 we …

Let M be a smooth closed Riemannian manifold and∆ the Laplace operator. A function u is
said to be an eigenfunction with eigenvalue λ if∆ u=− λu.(0.1) With our convention on the …

Let u be a harmonic function in the unit ball B(0,1)⊂R^n, n≥3, such that u(0)=0. Nadirashvili
conjectured that there exists a positive constant c, depending on the dimension n only, such …

The implicit function theorem implies that the nodal set of a smooth function, the set where
the function vanishes, is a smooth hypersurface away from the critical nodal set, or the …

Let $\ncal_ {\phi_ {\lambda}} $ be the nodal hypersurface of a $\Delta $-eigenfunction $\phi_
{\lambda} $ of eigenvalue $\lambda^ 2$ on a smooth Riemannian manifold. We prove the …

Suppose that φ is an eigenfunction of− Δ with eigenvalue λ≠ 0. It is proved that‖ φ‖∞⩽
c1λn− 1 4‖ φ‖ 2, where n is the dimension of M and c1 depends only upon a bound for the …

arXiv:1205.2812v1 [math.SP] 12 May 2012 Page 1 EIGENFUNCTIONS AND NODAL SETS
STEVE ZELDITCH Abstract. This is a survey of recent results on nodal sets of eigenfunctions …

Suppose that $ M $ is a compact Riemannian manifold with boundary and $ u $ is an $ L^
2$-normalized Dirichlet eigenfunction with eigenvalue $\lambda $. Let $\psi $ be its normal …