Sharp Uniform Thresholds for a Two-Parameter Power-Function Inequality

A symmetric two-parameter power-function defect has a sharp threshold for nonnegativity on upper squares. The threshold is characterized by one scalar equation, decreases with dimension, and is asymptotic to two divided by the square of the dimension. The proof gives the equality cases, the unique sign change below threshold, and a simplex-volume interpretation.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-02
DOI
https://doi.org/10.5281/zenodo.23887928
Primary Topic
Mathematical Inequalities and Applications
Type
preprint
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preprint

Sharp Uniform Thresholds for a Two-Parameter Power-Function Inequality

Ziping Guo
Zenodo (CERN European Organization for Nuclear Research)
Mathematical Inequalities and Applications
preprint

Sharp Uniform Thresholds for a Two-Parameter Power-Function Inequality

Ziping Guo
preprint en

Abstract

A symmetric two-parameter power-function defect has a sharp threshold for nonnegativity on upper squares. The threshold is characterized by one scalar equation, decreases with dimension, and is asymptotic to two divided by the square of the dimension. The proof gives the equality cases, the unique sign change below threshold, and a simplex-volume interpretation.

Zenodo (CERN European Organization for Nuclear Research)
Mathematical Inequalities and Applications
DOIOpen Access PDFOpenAlex
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Sharp Uniform Thresholds for a Two-Parameter Power-Function Inequality — Ziping Guo · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS