Related papers: Free energy minimizers with radial densities: clas…

For a given family of smooth closed curves $\gamma^1,...,\gamma^\alpha\subset\mathbb{R}^3$ we consider the problem of finding an elastic \emph{connected} compact surface $M$ with boundary $\gamma=\gamma^1\cup...\cup\gamma^\alpha$. This is…

We solve explicitly a certain minimization problem for probability measures involving an interaction energy that is repulsive at short distances and attractive at large distances. We complement earlier works by showing that part of the…

We reformulate the covering and quantizer problems as the determination of the ground states of interacting particles in $\mathbb{R}^d$ that generally involve single-body, two-body, three-body, and higher-body interactions. This is done by…

We consider spherically symmetric static solutions of the Einstein equations with a positive cosmological constant $\Lambda,$ which are regular at the centre, and we investigate the influence of $\Lambda$ on the bound of M/R, where M is the…

We prove that in any rank one symmetric space of non-compact type $M\in\{\mathbb{R} H^n,\mathbb{C} H^m,\mathbb{H} H^m,\mathbb{O} H^2\}$, geodesic spheres are uniformly quantitatively stable with respect to small $C^1$-volume preserving…

We study global minimizers of a functional modeling the free energy of thin liquid layers over a solid substrate under the combined effect of surface, gravitational, and intermolecular potentials. When the latter ones have a mild repulsive…

Equilibrium shapes of two-dimensional charged, perfectly conducting liquid drops are governed by a geometric variational problem that involves a perimeter term modeling line tension and a capacitary term modeling Coulombic repulsion. Here…

We consider a class of attractive-repulsive energies, given by the sum of two nonlocal interactions with power-law kernels, defined over sets with fixed measure. It has recently been proved by R. Frank and E. Lieb that the ball is the…

We prove that, for any measurable phase space subset $\Omega\subset\mathbb{R}^{2d}$ with $0<|\Omega|<\infty$ and any $1\le p < \infty$, the nonlinear concentration problem $$ \sup_{f \in…

The main objective of this article is to study the viable compact stellar structures in non-Riemannian geometry, i.e., $f(\mathbb{Q},T)$ theory, where $\mathbb{Q}$ defines the non-metricity and $T$ represents trace of the stress-energy…

On a Riemannian manifold with a positive lower bound on the Ricci tensor, the distance of isoperimetric sets from geodesic balls is quantitatively controlled in terms of the gap between the isoperimetric profile of the manifold and that of…

We introduce a new variational method for the study of stability in the isoperimetric inequality. The method is quite general as it relies on a penalization technique combined with the regularity theory for quasiminimizers of the perimeter.…

We show the counter-intuitive fact that some weighted isoperimetric problems on the half-space $ \mathbb{R}^N _+ $, for which half-balls centered at the origin are stable, have no solutions. A particular case is the measure $d\mu = x_N…

We study the symmetry and uniqueness of maps which minimise the $np$-Dirichlet energy, under the constraint that their Jacobian is a given radially symmetric function $f$. We find a condition on $f$ which ensures that the minimisers are…

We study a new class of equilibrium two-parametric distribution functions of spherical stellar systems with radially anisotropic velocity distribution of stars. The models are less singular counterparts of the so called generalized…

We establish an energy quantization for constrained Willmore surfaces, where the constraints are given by area, volume, and total mean curvature, assuming that the underlying conformal structures remain bounded. Furthermore, we show strong…

We address in this work the problem of minimizing quantum entropies under local constraints. We suppose macroscopic quantities such as the particle density, current, and kinetic energy are fixed at each point of $\Rm^d$, and look for a…

We consider the minimizers of the energy $$ \|u\|_{H^s(\Omega)}^2+\int_\Omega W(u)\,dx,$$ with $s \in (0,1/2)$, where $\|u\|_{H^s(\Omega)}$ denotes the total contribution from $\Omega$ in the $H^s$ norm of $u$, and $W$ is a double-well…

We consider the "thin one-phase" free boundary problem, associated to minimizing a weighted Dirichlet energy of the function in $\mathbb R^{n+1}_+$ plus the area of the positivity set of that function in $\mathbb R^n$. We establish full…

Let $K$ be a convex polyhedron and $\mathscr F$ its Wulff energy, and let $\mathscr C(K)$ denote the set of convex polyhedra close to $K$ whose faces are parallel to those of $K$. We show that, for sufficiently small $\epsilon$, all…