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arXiv · 2501.08782

A CR structure with blowing up solutions to the CR Yamabe problem

Claudio Afeltra·Andrea Pinamonti
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Abstract

We prove the existence of a CR structure on $S^3$ such that the set of solutions to the CR Yamabe problem is not compact and admits a blowing-up sequence. Such CR structure is built deforming the standard CR structure of $S^3$ in the direction of the Rossi sphere CR structure on small balls, and the existence of the blowing-up sequence of solutions is proved through the Lyapunov-Schmidt method.

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Claudio Afeltra, Andrea Pinamonti. 2025-01-15. A CR structure with blowing up solutions to the CR Yamabe problem. https://arxiv.org/abs/2501.08782

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