Related papers: Korn type Inequalities for Objective Structures

There is a lot of information available concerning Hardy-Hilbert type inequalities in one or more dimensions. In this paper we introduce the development of such inequalities on homogeneous groups. Moreover, we point out a unification of…

Coarse geometry studies metric spaces on the large scale. Our goal here is to study dynamics from a coarse point of view. To this end we introduce a coarse version of topological entropy, suitable for unbounded metric spaces, consistent…

We show that the mapping class group of a compact orientable surface with higher complexity has the following extreme rigidity in the sense of measure equivalence: if the mapping class group is measure equivalent to a discrete group, then…

Working over imperfect fields, we give a comprehensive classification of genus-one curves that are regular but not geometrically regular, extending the known case of geometrically reduced curves. The description is given intrinsically, in…

We establish a family of parametric isoperimetric-type inequalities with multiple geometric quantities for closed convex curves. These inequalities hold under certain parameter conditions. We also prove the equality conditions. Some new…

We prove a family of $L^p$ uncertainty inequalities on fairly general groups and homogeneous spaces, both in the smooth and in the discrete setting. The crucial point is the proof of the $L^1$ endpoint, which is derived from a general weak…

We prove several interesting equalities for the integrals of higher order derivatives on the homogeneous groups. As consequences, we obtain the sharp Hardy--Rellich type inequalities for higher order derivatives including both the…

We prove several stability and volume difference inequalities for projections of convex bodies and apply them to prove a hyperplane inequality for surface area of projection bodies.

Elucidating long-range interaction guided organization of matter is a fundamental question in physical systems covering multiple length scales. Here, based on the hexagonal disk model, we analyze the characteristic inhomogeneity created by…

Methods for calculating an electron density of a periodic crystal constructed using non-orthogonal localised orbitals are discussed. We demonstrate that an existing method based on the matrix expansion of the inverse of the overlap matrix…

The concept of p-orthogonality (1=< p =< n) between n-particle states is introduced. It generalizes common orthogonality, which is equivalent to n-orthogonality, and strong orthogonality between fermionic states, which is equivalent to…

Characterization results for equality cases and for rigidity of equality cases in Steiner's perimeter inequality are presented. (By rigidity, we mean the situation when all equality cases are vertical translations of the Steiner's symmetral…

Necessary and sufficient conditions are exhibited for a Korn type inequality to hold between (possibly different) Orlicz norms of the gradient of vector-valued functions and of the deviatoric part of their symmetric gradients. As a…

This paper extends our earlier results to higher dimensions using a different approach, based on the rigidity of complex structures on certain domains.

Developing a reliable kinetic energy density functional within orbital-free density functional theory remains a long-standing challenge, particularly for atomic and molecular systems. A major difficulty lies in the absence of a systematic…

Context. A porous and/or fractal description can generally be applied where particles have undergone coagulation into aggregates. Aims. To characterise finite-sized, porous and fractal particles and to understand the possible limitations of…

We develop the structure theory of full isometry groups of locally compact non-positively curved metric spaces. Amongst the discussed themes are de Rham decompositions, normal subgroup structure and characterising properties of symmetric…

Using group theory arguments, we demonstrate that, unlike in homogeneous media, no symmetric vortices of arbitrary order can be generated in two-dimensional (2D) nonlinear systems possessing a discrete-point symmetry. The only condition…

A discrete-to-continuum analysis for free-boundary problems related to crystalline films deposited on substrates is performed by $\Gamma$-convergence. The discrete model here introduced is characterized by an energy with two contributions,…

Physical systems are frequently modeled as sets of points in space, each representing the position of an atom, molecule, or mesoscale particle. As many properties of such systems depend on the underlying ordering of their constituent…