Compactness and blow up results for doubly perturbed Yamabe problems on manifolds with non umbilic boundary | Zendy

Marco Ghimenti | Zendy; Anna Maria Micheletti | Zendy

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Compactness and blow up results for doubly perturbed Yamabe problems on manifolds with non umbilic boundary

Author(s) -

Marco Ghimenti,

Anna Maria Micheletti

Publication year - 2022

Publication title -

electronic research archive

Language(s) - English

Resource type - Journals

ISSN - 2688-1594

DOI - 10.3934/era.2022064

Subject(s) - scalar curvature , mathematics , compact space , curvature , boundary (topology) , mathematical analysis , yamabe flow , mean curvature , riemannian manifold , manifold (fluid mechanics) , mean curvature flow , sectional curvature , geometry , mechanical engineering , engineering

We study the stability of compactness of solutions for the Yamabe boundary problem on a compact Riemannian manifold with non umbilic boundary. We prove that the set of solutions of Yamabe boundary problem is a compact set when perturbing the mean curvature of the boundary from below and the scalar curvature with a function whose maximum is not too positive. In addition, we prove the counterpart of the stability result: there exists a blowing up sequence of solutions when we perturb the mean curvature from above or the mean curvature from below and the scalar curvature with a function with a large positive maximum.

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