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arXiv · 2601.08804

Price Inequality and the Growth of Harmonic Functions on Non-Positively Curved Manifolds

Luca F. Di Cerbo·Hayden Hunter·Aaron K. Thrasher
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Abstract

We obtain effective estimates for the growth rate of the $L^2$-energy of harmonic functions on geodesic balls in complete simply connected non-positively curved Riemannian manifolds with pinched sectional curvature. Our study relies upon a double-sided Price inequality for harmonic functions. Finally, we apply this circle of ideas to study the analytical structure of a potential counterexample to the Singer conjecture in degree one.

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Luca F. Di Cerbo, Hayden Hunter, Aaron K. Thrasher. 2026-01-13. Price Inequality and the Growth of Harmonic Functions on Non-Positively Curved Manifolds. https://arxiv.org/abs/2601.08804

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