Abstract We solve time-harmonic Maxwell’s equations in anisotropic, spatially homogeneous media intersections of $$L^p$$ L p -spaces. The material laws are time-independent. analysis requires Fourier restriction–extension estimates for perturbations Fresnel’s wave surfa...

Building on the recently introduced notion of quantum Ricci curvature and motivated by considerations in nonperturbative gravity, we advocate a new, global observable for curved metric spaces, profile. It is obtained integrating scale-dependent, quasilocal curvature, therefore also depends coarse-graining scale. To understand how distribution local, Gaussian reflected profile, compute it class ...

The elastic theory of a uniaxial membrane in an asymmetric environment predicts a spontaneous splay deformation. This spontaneous curvature of the membrane is discussed by the intrinsic splay of the membrane molecules (e.g. wedge shaped molecules) and their polar orientation. The chemoelastic effect if the polar orientation induced by the asymmetric environment in connection with the intrinsic ...

Conical inclusions in a lipid bilayer generate an overall spontaneous curvature of the membrane that depends on concentration and geometry of the inclusions. Examples are integral and attached membrane proteins, viruses, and lipid domains. We propose an analytical model to study budding and vesiculation of the lipid bilayer membrane, which is based on the membrane bending energy and the transla...

Vibrational sum frequency generation (VSFG) spectroscopy was used to study the nanoscale geometric effects on molecular conformation of dodecanethiol ligand on gold nanoparticles of varying size between 1.8 and 23 nm. By analyzing the CH3 and CH2 stretch transitions of dodecanethiol using the spectroscopic propensity rules for the SFG process, we observe the increase of the gauche defects in th...

Abstract We show that the singularities of twisted Kähler–Einstein metric arising as longtime solution Kähler–Ricci flow or in collapsed limit Ricci-flat Kähler metrics are intimately related to holomorphic sectional curvature reference conical geometry. This provides an alternative proof second-order estimate obtained by Gross, Tosatti, and Zhang (2020, Preprint, arXiv:1911.07315) with explici...

We prove that a compact stratified space satisfies the Riemannian curvature-dimension condition RCD(K,N) if and only its Ricci tensor is bounded below by K?? on regular set, cone angle along stratum of codimension two smaller than or equal to 2? dimension at most N. This gives new wide class geometric examples metric measure spaces satisfying condition, including for instance spherical suspensi...

Point sources in (2+1)-dimensional gravity are conical singularities that modify the global curvature of the space giving rise to selfinteraction effects on classical fields. In this work we study the electrostatic self-interaction of a point charge in the presence of point masses in (2+1)-dimensional gravity with a cosmological constant Λ. Exact expressions are obtained for the self-force on t...