Double bubbles with high constant mean curvatures in Riemannian manifolds. (November 2022)

• Record Type: Journal Article
• Authors: Di Matteo, Gianmichele; Malchiodi, Andrea
• Is Part Of: Nonlinear analysis. Volume 224(2022)
• Publication Date: 2022-11
• Subjects: 55J20 -- 35B40 -- 53A10 -- 53C42; Double bubbles -- Constant mean curvature -- Isoperimetric problems; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.113088
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We obtain existence of double bubbles of large and constant mean curvatures in Riemannian manifolds. These arise as perturbations of geodesic standard double bubbles centered at critical points of the ambient scalar curvature and aligned along eigen-vectors of the ambient Ricci tensor. We also obtain general multiplicity results via Lusternik–Schnirelman theory, and extra ones in case of double bubbles whose opposite boundaries have the same mean curvature.