The double and triple bubble problem for stationary varifolds: the convex case

Abstract

We characterize the critical points of the double bubble problem in ${\mathbb{R}}^n$ and the triple bubble problem in ${\mathbb{R}}^3$, in the case the bubbles are convex.

References in corpus (9)

• Proof of the Double Bubble Conjecture in R^n
• Alexandrov's theorem revisited
• Symmetry via Spherical Reflection and Spanning Drops in a Wedge
• Bubbling with $L^2$-almost constant mean curvature and an Alexandrov-type theorem for crystals
• Uniqueness of critical points of the anisotropic isoperimetric problem for finite perimeter sets
• Absence of bubbling phenomena for non convex anisotropic nearly umbilical and quasi Einstein hypersurfaces
• Minimal clusters of four planar regions with the same area
• Uniqueness of singular convex hypersurfaces with lower bounded k-th mean curvature
• A Heintze-Karcher inequality with free boundaries and applications to capillarity theory