Double bubbles with high constant mean curvatures in Riemannian manifolds

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.