Related papers: M\"obius invariant energies and average linking wi…
Vacuum energy and other spectral functions of Laplace-type differential operators have been studied approximately by classical-path constructions and more fundamentally by boundary integral equations. As the first step in a program of…
In this paper, we prove power-saving bounds for the corelation of the M\"obius function with polynomial phases of degree $k$ in function fields $\mathbb{F}_p[t]$, when $p > k$. The proof relies on a new approximation result for phases of…
The goal of the present paper is to investigate the algebraic structure of global conformal invariants of submanifolds. These are defined to be conformally invariant integrals of geometric scalars of the tangent and normal bundle. A famous…
A generalized form of 't Hooft-Nobbenhuis Complex space-time Transformation is applied on momentum space from which a new model of Deformed Special Relavity at Planck Scale is proposed. The model suggests an energy-dependent Planck's…
Starting with a pseudo-Anosov flow $\varphi$ on a closed hyperbolic $3$-manifold $M$ and an embedded surface $S \subset M$ that is (almost) transverse to $\varphi$, we relate the hyperbolic geometry of $M$ (e.g. volume, circumference, short…
The component form of the equations of motion for the 5-brane in eleven-dimensions is derived from the superspace equations. These equations are fully covariant in six-dimensions. It is shown that double-dimensional reduction of the bosonic…
Adaptation of the Hamilton--Jacobi formalism to quantum mechanics leads to a cocycle condition, which is invariant under $D$--dimensional M\"obius transformations with Euclidean or Minkowski metrics. In this paper we aim to provide a…
We denote by $\mathbb{M}^2_R$ a two dimensional space of constant positive Gaussian curvature. With methods of M\"obius geometry and using the classification of the M\"obius group of automorphisms ${\rm \bf Mob}_2 \, (\hat{\mathbb{C}})$ of…
We study the Beurling and Fourier transforms on subspaces of $L^2({\mathbb C})$ defined by an invariance property with respect to the root-of-unity group. This leads to generalizations of these transformations acting unitarily on weighted…
O'Hara introduced several functionals as knot energies. One of them is the M\"{o}bius energy. We know its M\"{o}bius invariance from Doyle-Schramm's cosine formula. It is also known that the M\"{o}bius energy was decomposed into three…
To an ergodic, essentially free and measure-preserving action of a non-amenable Baumslag-Solitar group on a standard probability space, a flow is associated. The isomorphism class of the flow is shown to be an invariant of such actions of…
We consider how to describe Hamiltonian mechanics in generalised probabilistic theories with the states represented as quasi-probability distributions. We give general operational definitions of energy-related concepts. We define…
m-Qubit states are imbedded in $\mathfrak{Cl}_{2^m}$ Clifford algebras. Their probability spectra then depend on $O(2m)$ or $O(2m+1)$ invariants. Parameter domains for $O(2m(+1))-$ vector and tensor configurations, generalizing the notion…
We consider the geometry of the space of Borel measures endowed with a distance that is defined by generalizing the dynamical formulation of the Wasserstein distance to concave, nonlinear mobilities. We investigate the energy landscape of…
In this paper, we define a new conformal invariant on complete non-compact hyperbolic surfaces that can be conformally compactified to bounded domains in $\mathbb{C}$. We study and compute this invariant up to one-connected surfaces. Our…
In addition to inherent computational challenges, the absence of a canonical method for quantifying `persistence' in multi-parameter persistent homology remains a hurdle in its application. One of the best known quantifications of…
We construct a covariant bound on the energy-momentum of the M-fivebrane which is saturated by all supersymmetric configurations. This leads to a generalised notion of a calibrated geometry for M-fivebranes when the worldvolume gauge field…
Generalisations of the relativistic ideal Ohm's law are presented that include specific dynamical features of the current carrying particles in a plasma. Cases of interest for space and laboratory plasmas are identified where these…
In this paper we use the theory of $\epsilon$-constants associated to tame finite group actions on arithmetic surfaces to define a Brauer group invariant $\mu(\X,G,V)$ associated to certain symplectic motives of weight one. We then discuss…
We characterize the class of Gromov hyperbolic spaces, whose boundary at infinity allow canonical M\"obius structures.