Accepted Paper

Inserted: 22 jan 2024
Last Updated: 14 jun 2024

Journal: International Mathematics Research Notices
Year: 2024

Abstract:

We obtain a vanishing result for solutions of the inequality $\vert \Delta u \vert ≤ q_1\vert u\vert+ q_2\vert \nabla u\vert$ that decay to zero along a very general warped cylindrical end of a Riemannian manifold. The appropriate decay condition at infinity on $u$ is related to the behavior of the potential functions $q_1$ and $q_2$ and to the asymptotic geometry of the end. The main ingredient is a new Carleman estimate of independent interest. Geometric applications to conformal deformations and to minimal graphs are presented.

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