In this paper, we prove an extended version of the Minkowski Inequality, holding for any
smooth bounded set Ω⊂ R n, n≥ 3. Our proof relies on the discovery of effective …

The distance of an almost‐constant mean curvature boundary from a finite family of disjoint
tangent balls with equal radii is quantitatively controlled in terms of the oscillation of the …

The question of isoperimetry What is the largest amount of volume that can be enclosed by a
given amount of area? can be traced back to antiquity. 1 The first mathematically rigorous …

Motivated by a model for lipid bilayer cell membranes, we study the minimization of the
Willmore functional in the class of oriented closed surfaces with prescribed total mean …

A compactness theorem for volume-constrained almost-critical points of elliptic integrands is
proven. The result is new even for the area functional, as almost-criticality is measured in an …

The goal of this paper is to establish the existence of a foliation of the asymptotic region of
an asymptotically flat manifold with positive mass by surfaces which are critical points of the …

We construct 2-surfaces of prescribed mean curvature in 3-manifolds carrying asymptotically
flat initial data for an isolated gravitating system with rather general decay conditions. The …

We prove the following quantitative version of the celebrated Soap Bubble Theorem of
Alexandrov. Let S be a C2 closed embedded hypersurface of Rn+ 1, n≥ 1, and denote by …

We consider a range of geometric stability problems for hypersurfaces of spaceforms. One of
the key results is an estimate relating the distance to a geodesic sphere of an embedded …

Let (M, g) be an asymptotically flat Riemannian 3‐manifold with nonnegative scalar
curvature and positive mass. We show that each leaf of the canonical foliation of the end of …