Lower bounds for volumes of nodal sets: an improvement of a result of Sogge-Zelditch
Hamid Hezari, Zuoqin Wang
TL;DR
This paper improves lower bounds on the volume of nodal sets of eigenfunctions using the Dong-Sogge-Zelditch formula, providing new insights especially in dimensions up to five.
Contribution
It introduces an improved lower bound for nodal set volumes by leveraging the Dong-Sogge-Zelditch formula, enhancing previous results by Sogge-Zelditch.
Findings
Enhanced lower bounds for nodal set volumes in certain dimensions
New proof for bounds established by Colding-Minicozzi in dimensions n ≤ 5
Application of the Dong-Sogge-Zelditch formula to eigenfunction analysis
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 n \leq 5 gives a new proof for the lower bounds of Colding-Minicozzi.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Geometric Analysis and Curvature Flows · Numerical methods in inverse problems