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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
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 .