| Autor: |
Bisterzo, Andrea, Farina, Alberto, Pigola, Stefano |
| Rok vydání: |
2023 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
On a complete Riemannian manifold $(M,g)$, we consider $L^{p}_{loc}$ distributional solutions of the the differential inequality $-\Delta u + \lambda u \geq 0$ with $\lambda >0$ a locally bounded function that may decay to $0$ at infinity. Under suitable growth conditions on the $L^{p}$ norm of $u$ over geodesic balls, we obtain that any such solution must be nonnegative. This is a kind of generalized $L^{p}$-preservation property that can be read as a Liouville type property for nonnegative subsolutiuons of the equation $\Delta u \geq \lambda u$. An application of the analytic results to $L^{p}$ growth estimates of the extrinsic distance of complete minimal submanifolds is also given. |
| Databáze: |
arXiv |
| Externí odkaz: |
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