The size of the nodal sets for the eigenfunctions of the smooth laplacian
Demetrios A. Pliakis
TL;DR
This paper provides estimates for eigenfunctions on smooth manifolds and uses these to determine the size of their nodal sets, advancing understanding of eigenfunction behavior in geometric analysis.
Contribution
It introduces new estimates for eigenfunctions on smooth manifolds and applies them to quantify the size of their nodal sets, a novel approach in geometric analysis.
Findings
Quantitative bounds on eigenfunction estimates
Size estimates for nodal sets of eigenfunctions
Application of estimates to geometric analysis
Abstract
We prove estimates for eigenfunctions on a manifold equipped with a smooth metric. We use these estimates in order estimate the size of their nodal sets.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Nonlinear Partial Differential Equations