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arXiv · 2409.07502

A Bogovski\v{i}-type operator for Corvino-Schoen hyperbolic gluing

Piotr T. Chruściel·Albachiara Cogo·Andrea Nützi
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Abstract

We construct a solution operator for the linearized constant scalar curvature equation at hyperbolic space in space dimension larger than or equal to two. The solution operator has good support propagation properties and gains two derivatives relative to standard norms. It can be used for Corvino-Schoen-type hyperbolic gluing, partly extending the recently introduced Mao-Oh-Tao gluing method to the hyperbolic setting.

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Piotr T. Chruściel, Albachiara Cogo, Andrea Nützi. 2024-09-10. A Bogovski\v{i}-type operator for Corvino-Schoen hyperbolic gluing. https://doi.org/10.1088/1361-6382/adda88

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