Price Inequality and the Growth of Harmonic Functions on Non-Positively Curved Manifolds
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.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Advanced Differential Geometry Research
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 13 January 2026
- Document type
- Preprint