Average estimate for Eigenfunctions along geodesics in the quantum completely integrable case

Weiwei Wang; Xianchao Wu

Average estimate for Eigenfunctions along geodesics in the quantum completely integrable case

Analysis of PDEs 2026-04-08 v2

Authors: Weiwei Wang , Xianchao Wu

Abstract

This paper investigates the upper bound of the integral of $L^2$ -normalized joint eigenfunctions over geodesics in a two-dimensional quantum completely integrable system. For admissible geodesics, we rigorously establish an asymptotic decay rate of $O(h^{1/2})$ . This represents a polynomial improvement over the previously well known $O(1)$ bound.

Keywords

laplacian eigenfunctions geodesics and riemannian geometry

Cite

@article{arxiv.2506.15992,
  title  = {Average estimate for Eigenfunctions along geodesics in the quantum completely integrable case},
  author = {Weiwei Wang and Xianchao Wu},
  journal= {arXiv preprint arXiv:2506.15992},
  year   = {2026}
}

Comments

We have improved the previous result and modified the examples in the Section 3

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