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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Sharp Lp estimates and size of nodal sets of generalized Steklov eigenfunctions
Steklov-eigenfunctions 尖锐 Lp 估计 节点集
2023/4/13
We prove sharp Lp estimates for the Steklov eigenfunctions on compact manifolds with boundary in terms of their L2 norms on the boundary. We prove it by establishing Lp bounds for the harmonic extensi...
A natural lower bound for the size of nodal sets
natural lower bound size of nodal sets Analysis of PDEs
2011/9/14
Abstract: We prove a natural inequality which implies the known lower bounds for the $(n-1)$-dimensional Hausdorff measure of nodal sets for smooth compact manifolds.
Lower bounds for volumes of nodal sets: an improvement of a result of Sogge-Zelditch
Lower bounds volumes of nodal sets Sogge-Zelditch
2011/8/22
Abstract: We use the Dong-Sogge-Zelditch formula to obtain a lower bound for the volume of the nodal sets of eigenfunctions. Our result improves the recent results of Sogge-Zelditch and in dimensions ...
Lower bounds on the Hausdorff measure of nodal sets
Lower bounds Hausdorff measure of nodal sets
2010/12/8
Let N' be the nodal hypersurface of a -eigenfunction ' of eigenvalue 2on a smooth Riemannian manifold. We prove that Hn−1(N') ≥ C7 4− 3n 4 on the surface measure of its nodal set. Th...
Let M be a smooth closed Riemannian manifold and the Laplace operator. A function u is said to be an eigenfunction with eigenvalue if u = − u .