Calculus of Variations and Geometric Measure Theory

G. Di Matteo - A. Malchiodi

Double Bubbles with High Constant Mean Curvatures in Riemannian Manifolds

created by malchiodi on 22 Dec 2021
modified on 01 Aug 2022


Accepted Paper

Inserted: 22 dec 2021
Last Updated: 1 aug 2022

Journal: Nonlin. Anal., to appear.
Pages: 37
Year: 2021

ArXiv: 2112.08269 PDF


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.