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

2021/12/08 by Marco Ghimenti, Ghimenti, Marco G., Anna Maria Micheletti +1
Computer Science · Mathematics · #35J65 #53C21 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2112.04207

openalex publication_date 2021/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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