Related papers: A strong form of the quantitative Wulff inequality
We investigate surfaces with bounded L^p-norm of the fractional mean curvature, a quantity we shall refer to as fractional Willmore-type functional. In the subcritical case and under convexity assumptions we show how this…
We establish regularity results for almost-minimizers of a class of variational problems involving both bulk and interface energies. The bulk energy is of Dirichlet type. The surface energy exhibits anisotropic behaviour and is defined by…
Electrons mediate many of the interactions between atoms in a solid. Their propagation in a material determines its thermal, electrical, optical, magnetic and transport properties. Therefore, the constant energy contours characterizing the…
Using finite difference operators, we define a notion of boundary and surface measure for configuration sets under Poisson measures. A Margulis-Russo type identity and a co-area formula are stated with applications to deviation inequalities…
A generalization of the affine-geometric Wirtinger inequality for curves to hypersurfaces is given.
This paper studies the effect of anisotropy on sharp or diffuse interfaces models. When the surface tension is a convex function of the normal to the interface, the anisotropy is said to be weak. This usually ensures the lower…
We study Hawking mass and the Huisken's isoperimetric mass evaluated on surfaces with boundary. The convergence to an ADM mass defined on asymptotically flat manifold with a non-compact boundary are proved.
We introduce a rigorous approach to the study of the symmetry breaking and pattern formation phenomenon for isotropic functionals with local/nonlocal interactions in competition. We consider a general class of nonlocal variational problems…
Independent random signs can govern various discrete models that converge to non-isomorphic continuous limits. Convergence of Fourier-Walsh spectra is established under appropriate conditions.
A new proof of the Wulff-Gage isoperimetric inequality for origin-symmetric convex bodies is provided. As its applications, we prove the uniqueness of log-Minkowski problem and a new proof of the log-Minkowski inequality of curvature…
In this paper, we prove a quantitative refinement of the isoperimetric type inequality for the second Robin eigenvalue with negative boundary parameters established by Freitas and Laugesen [Amer.J.Math.143 (2021), no.3, 969-994].Such new…
A new phenomenon is observed experimentally in a heavily doped asymmetric quantum-size structure in a magnetic field parallel to the quantum-well layers - a transverse magnetoresistance which is asymmetric in the field (there can even be a…
We review and extend here some recent results on the existence of minimal surfaces and isoperimetric sets in non homogeneous and anisotropic periodic media. We also describe the qualitative properties of the homogenized surface tension,…
The presence of dark energy in the Universe is inferred directly from the accelerated expansion of the Universe, and indirectly, from measurements of cosmic microwave background (CMB) anisotropy. Dark energy contributes about 2/3 of the…
The problem of measurement in quantum mechanics is studied within the Entropic Dynamics framework. We discuss von Neumann and Weak measurements, wavefunction collapse, and Weak Values as examples of bayesian and entropic inference.
We exhibit three inequalities involving quantum measurement, all of which are sharp and state independent. The first inequality bounds the performance of joint measurement. The second quantifies the trade-off between the measurement quality…
The problem of anisotropic pressures arising as a consequence of the spatial symmetry breaking introduced by an external magnetic field in quantum systems is discussed. The role of the conservation of energy and momentum of external fields…
Recent analyses of the first-year WMAP data claim large-scale asymmetry and anisotropy of the CMBR fluctuations. We argue that the covariant and gauge invariant treatment of density fluctuations formulated by Ellis and Bruni can explain the…
In this paper, we investigate the extremal functions for anisotropic Trudinger-Moser inequalities. Our method uses convex symmetrization, the continuity of the supremum function, together with the relation between the supremums of the…
We investigate isoperimetric constants of infinite tessellating metric graphs. We introduce a curvature-like quantity, which plays the role of a metric graph analogue of discrete curvature notions for combinatorial tessellating graphs. We…