Unique continuation at infinity: Carleman estimates on general warped cylinders

Nicolò De Ponti; Stefano Pigola; Giona Veronelli

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arXiv · 2401.12367

Unique continuation at infinity: Carleman estimates on general warped cylinders

Nicolò De Ponti·Stefano Pigola·Giona Veronelli

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Abstract

We obtain a vanishing result for solutions of the inequality $|\Delta u|\le q_1|u|+q_2|\nabla u|$ 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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Nicolò De Ponti, Stefano Pigola, Giona Veronelli. 2024-01-22. Unique continuation at infinity: Carleman estimates on general warped cylinders. https://arxiv.org/abs/2401.12367

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