Related papers: Peeling in Generalized Harmonic Gauge
We prove that the convex peeling of a random point set in dimension d approximates motion by the 1/(d + 1) power of Gaussian curvature. We use viscosity solution theory to interpret the limiting partial differential equation. We use the…
Tangent measure and blow-up methods, are powerful tools for understanding the relationship between the infinitesimal structure of the boundary of a domain and the behavior of its harmonic measure. We introduce a method for studying tangent…
Present and future high-precision tests of the Standard Model and beyond for the fundamental constituents and interactions in Nature are demanding complex perturbative calculations involving multi-leg and multi-loop Feynman diagrams.…
We study the application of generalized symmetry for reducing nonlinear partial differential equations. We construct the ansatzes for dependent variable $u$ which reduce the scalar partial differential equation with two independent…
Basic aspects of the Hamiltonian structure of the parity-violating Poincar\'e gauge theory are studied. We found all possible primary constraints, identified the corresponding critical parameters, and constructed the generic form of the…
In this work we explore the effects of nonlinearity on three-dimensional topological phases. Of particular interest are the so-called Weyl semimetals, known for their Weyl nodes, i.e., point-like topological charges which always exist in…
[1] investigates advanced connotations of Hardy and Rellich-type inequalities on complete noncompact Riemannian manifolds, delving on deriving inequalities that incorporate poignant weight functions. These inequalities prolongate classical…
We perform a systematic analysis of the conditions under which \textit{generalized} gauge field theories of compact semisimple Lie groups exhibit electrostatic spherically symmetric non-topological soliton solutions in three space…
This paper introduces a grand canonical mixture model to generalize the nonideal Rayleigh gas [5] to an asymptotically infinite amount of perturbed tagged particles. This model relies precisely on grand canonical tags, to preserve symmetry…
A Weyl structure is usually defined by an equivalence class of pairs $({\bf g}, \boldsymbol{\omega})$ related by Weyl transformations, which preserve the relation $\nabla {\bf g}=\boldsymbol{\omega}\otimes{\bf g}$, where ${\bf g}$ and…
Several models of quantum gravity predict the emergence of a minimal length at Planck scale. This is commonly taken into consideration by modifying the Heisenberg Uncertainty Principle into the Generalized Uncertainty Principle. In this…
The convex hull peeling of a point set consists in taking the convex hull, then removing the extreme points and iterating that procedure until no point remains. The boundary of each hull is called a layer. Following on from [15], we study…
One-dimensional optical waveguiding is revisited using the electromagnetic deduction of Fresnel formulas relating the incident, reflected, and transmitted waves on the abrupt interface between two different optical media. Throughout the…
We observe that the radial gauge can be consistently imposed \emph{together} with the Lorenz gauge in Maxwell theory, and with the harmonic traceless gauge in linearized general relativity. This simple observation has relevance for some…
Phase gradient metagratings/metasurfaces (PGMs) have provided a new paradigm for light manipulations. In this work, we will show the existence of gauge invariance in PGMs, i.e., the diffraction law of PGMs is independent of the choice of…
We start by studying a peeling process on finite random planar maps with faces of arbitrary degrees determined by a general weight sequence, which satisfies an admissibility criterion. The corresponding perimeter process is identified as a…
Firstly we derive peculiar spherical Weyl solutions, using a general spherically symmetric metric due to a massive charged object with definite mass and radius. Afterwards, we present new analytical solutions for relevant cosmological…
We study the mean-value harmonic functions on open subsets of $\mathbb{R}^n$ equipped with weighted Lebesgue measures and norm induced metrics. Our main result is a necessary condition saying that all such functions solve a certain…
We show how to determine the unknown functions arising when the peeling decomposition is applied to multi-critical matter coupled to two-dimensional quantum gravity and compute the loop-loop correlation functions. The results that…
We develop a unified approach for establishing rates of decay for the Fourier transform of a wide class of dynamically defined measures. Among the key features of the method is the systematic use of the $L^2$-flattening theorem obtained in…