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arXiv · 2503.09801

Quantitative Stability for Yamabe minimizers on manifolds with boundary

Benjamín Borquez·Rayssa Caju·Hanne Van Den Bosch
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Abstract

This paper addresses the quantitative stability for a Yamabe-type functional on compact manifolds with boundary introduced by Escobar. Minimizers of the functional correspond to scalar-flat metrics with constant mean curvature on the boundary. We prove that the deficit controls the distance to the minimizing set to a suitable power by reducing the problem to the analogous question for an effective functional on the boundary.

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Benjamín Borquez, Rayssa Caju, Hanne Van Den Bosch. 2025-03-12. Quantitative Stability for Yamabe minimizers on manifolds with boundary. https://arxiv.org/abs/2503.09801

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