Generalized existence results for the isoperimetric problem in Riemannian manifolds (Q2910000)

This short note is a summary of two papers of the author concerning the notion of isoperimetric profile of a Riemannian manifold and the notion of bubble. The author recalls a first theorem on the existence of bubbles of small volume, reducing an infinite-dimensional minimum problem to a finite-dimensional one. Then, he presents a second existence theorem for arbitrary volumes. Finally, he states a theorem which characterizes pseudo-bubbles with fixed center-mass and small volume.NEWLINENEWLINEFor the complete results see the author's papers [Ann. Global Anal. Geom. 36, No. 2, 111--131 (2009; Zbl 1175.53048); ``The isoperimetric profile of a noncompact Riemannian manifold for small volumes, Calc. Var. Partial Differ. Equ. (to appear; \url{doi:10.1007/s00526-012-0577-1})].