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Nodal-Length Bounds for Surface Metrics with Isolated Non-Analytic Points

Year: 2026

Type: preprint

Abstract: We prove a C_g sqrt(lambda) upper bound for nodal lengths on closed surfaces whose metrics are analytic away from finitely many isolated points and satisfy a summable quantitative analytic-scale condition near those points. The result includes an explicit smooth non-analytic torus family with Fourier coefficients exp(-|k|^alpha), 0 < alpha < 1. The theorem is a sufficient criterion for this structured class and does not resolve the corresponding upper bound for arbitrary smooth metrics.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.22901475

Authors: Jiang, Weiqi, Ye, Jintao

Institutions: Chinese Academy of Sciences, Institute of Theoretical Physics, Peking University

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7214017184

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