Calculus of Variations and Geometric Measure Theory

S. Nardulli

The isoperimetric profile of a smooth Riemannian manifold for small volumes

created by nardulli on 31 Jul 2019


Published Paper

Inserted: 31 jul 2019

Journal: Annals of Global Analysis and Geometry
Volume: 36
Number: 2
Pages: 111-131
Year: 2009
Doi: 10.1007/s10455-008-9152-6


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.