Related papers: Constrained energy problems with external fields
We present a new programme for placing constraints on radial inhomogeneity in a dark-energy dominated universe. We introduce a new measure to quantify violations of the Copernican principle. Any violation of this principle would interfere…
We introduce and study the unconstrained polarization (or Chebyshev) problem which requires to find an $N$-point configuration that maximizes the minimum value of its potential over a set $A$ in $p$-dimensional Euclidean space. This problem…
We present and discuss the bounds from the energy conditions on a general f(R) functional form in the framework of metric variational approach. As a concrete application of the energy conditions to locally homogeneous and isotropic…
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…
This paper is the continuation of [H. Kn\"upfer and C. B. Muratov, Commun. Pure Appl. Math. (2012, to be published)]. We investigate the classical isoperimetric problem modified by an addition of a non-local repulsive term generated by a…
We study minimum energy configurations of $N$ particles in $\R^3$ of charge -1 (`electrons') in the potential of $M$ particles of charges $Z_\alpha>0$ (`atomic nuclei'). In a suitable large-N limit, we determine the asymptotic electron…
We study the pinning of few-electron charge densities by weak perturbations to circular quantum ring potentials. We find that the pinning by weak defects is only allowed when the symmetry of the classical few-electron lowest-energy…
We consider $f(R)$ gravity theories which unify $R^n$ inflation and dark energy models. First, from the final Planck data of the cosmic microwave background, we obtain a condition, $1.977 < n < 2.003$. Next, under this constraint, we…
In this paper we consider the problem of characterizing the minimum energy configurations of a finite system of particles interacting between them due to attracting or repulsive forces given by a certain inter molecular potential. We limit…
We study the continuity and the measurability of the solution to Schr\"odinger's functional equation, with respect to space, kernel and marginals, provided the space of all Borel probability measures is endowed with the weak topology. This…
In this work, we extend the classical framework of quantization for Borel probability measures defined on normed spaces $\mathbb{R}^k$ by introducing and analyzing the notions of the $n$th constrained quantization error, constrained…
Low energy supersymmetry is motivated by its use as a solution to the hierarchy problem of the electroweak scale. Having motivated this model with naturalness arguments, it is then necessary to check whether the experimentally allowed…
We analyze the cosmology of the Randall-Sundrum model and that of compact brane models in general in the presence of a radius stabilization mechanism. We find that the expansion of our universe is generically in agreement with the expected…
Attention has been recently called upon the fact that the weak and null energy conditions and the second law of thermodynamics are violated in wormhole solutions of Einstein's theory with classical, nonminimally coupled, scalar fields as…
We analyze the properties of weakly compact sets in Lipschitz free spaces. Prior research has established that, for a complete metric space $M$, weakly precompact sets in the Lipschitz free space $\mathcal F(M)$ are tight. In this paper, we…
A fermion ground state energy functional is set up in terms of particle density, relative pair density, and kinetic energy tensor density. It satisfies a minimum principle if constrained by a complete set of compatibility conditions. A…
How to understand the set of correlations admissible in nature is one outstanding open problem in the core of the foundations of quantum theory. Here we take a complementary viewpoint to the device-independent approach, and explore the…
In this paper, we prove the existence of minimizers of a class of multi-constrained variational problems. We consider systems involving a nonlinearity that does not satisfy compactness, monotonicity, neither symmetry properties. Our…
A key test for any quasi-local energy in general relativity is that it be nonnegative and satisfy a rigidity property; if it vanishes, the region enclosed is flat. We show that the Hawking energy, when evaluated on its natural…
This paper explores recent progress related to constraint maps. Building on the exposition in [14], our goal is to provide a clear and accessible account of some of the more intricate arguments behind the main results in this work. Along…