Open AccessCompactness 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.