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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.08804 |
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| _version_ | 1866908845628981248 |
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| author | Di Cerbo, Luca F. Hunter, Hayden Thrasher, Aaron K. |
| author_facet | Di Cerbo, Luca F. Hunter, Hayden Thrasher, Aaron K. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08804 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Price Inequality and the Growth of Harmonic Functions on Non-Positively Curved Manifolds Di Cerbo, Luca F. Hunter, Hayden Thrasher, Aaron K. Differential Geometry 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. |
| title | Price Inequality and the Growth of Harmonic Functions on Non-Positively Curved Manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2601.08804 |