Inserted: 31 jul 2019
Journal: Annals of Global Analysis and Geometry
We define a new class of submanifolds called pseudo-bubbles, defined by an equation weaker than constancy of mean curvature. We show that in a neighborhood of each point of a Riemannian manifold, there is a unique family of concentric pseudo-bubbles which contains all the pseudo-bubbles C 2,α -close to small spheres. This permit us to reduce the isoperimetric problem for small volumes to a variational problem in finite dimension.