Related papers: Stability and integration over Bergman metrics

The objective of this paper is to derive the essential invariance and contraction properties for the geometric periodic systems, which can be formulated as a category of differential inclusions, and primarily rendered in the phase…

This paper presents a theoretical study of oscillatory and rotational instabilities of a solid spherical body, levitated electromagnetically in axisymmetric coils made of coaxial circular loops. We apply our previous theory to analyze the…

In this note, we consider the dynamics associated to an epsilon-perturbation of an integrable Hamiltonian system in action-angle coordinates in any number of degrees of freedom and we prove the following result of "micro-diffusion": under…

Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…

We study the quantization of coupled K\"ahler-Einstein (CKE) metrics, namely we approximate CKE metrics by means of the canonical Bergman metrics, so called the ``balanced metrics''. We prove the existence and weak convergence of balanced…

We model the phase oscillations of electrons in race-track microtrons by means of an area preserving map with a fixed point at the origin, which represents the synchronous trajectory of a reference particle in the beam. We study the…

We present the covariance analysis of two successful nuclear energy density functionals, (i) a non-relativistic Skyrme functional built from a zero-range effective interaction, and (ii) a relativistic nuclear energy density functional based…

We consider four dimensional lie groups equipped with left invariant Lorentzian Einstein metrics, and determine the harmonicity properties of vector fields on these spaces. In some cases, all these vector fields are critical points for the…

We study the perturbation of a measure $\mu \in \mathscr{P}(\mathbb{R})$ consisting in superposing two copies of $\mu$, each slightly shifted by a small distance $\pm h$. The difference between $\mu$ and its perturbation is measured with a…

This work discovers a novel link between probability theory (of stable random fields) and von Neumann algebras. It is established that the group measure space construction corresponding to a minimal representation is an invariant of a…

Let $R$ be a constant. Let $\mathcal{M}^R_\gamma$ be the space of smooth metrics $g$ on a given compact manifold $\Omega^n$ ($n\ge 3$) with smooth boundary $\Sigma $ such that $g$ has constant scalar curvature $R$ and $g|_{\Sigma}$ is a…

Using all available data on the deep-inelastic cross-sections at HERA at x<0.01, we look for geometric scaling of the form \sigma^{\gamma^*p}(\tau) where the scaling variable \tau behaves alternatively like \log(Q^2)-\lambda Y, as in the…

By constructing jointly a random graph and an associated exploration process, we define the dynamics of a "parking process" on a class of uniform random graphs as a measure-valued Markov process, representing the empirical degree…

The strong unique continuation property for Einstein metrics can be concluded from the well-known fact that Einstein metrics are analytic in geodesic normal coordinates. Here we give a proof of the same result that given two Einstein…

A new fundamental form of the path integral for theories with local symmetry is introduced. It is utilised to construct effective actions that generate correlation functions of dressed fields in Yang-Mills theories and quantum gravity. The…

Variational calculations using Gaussian wave functionals combined with an approximate projection on gauge invariant states are presented. We find that the energy exhibits a minimum for a wave functional centered around a non vanishing…

This is the first in a series of two papers studying mu-cscK metrics and muK-stability, from a new perspective evoked from observations in arXiv:2004.06393 and in this first article. The first paper is about a characterization of mu-cscK…

This paper is a summary of the general approach outlined in my previous papers toward proving the riemann hypothesis. Numerical and graphical proof of the Riemann Hypothesis is presented with analytical arguments although more work needs…

Functions which are covariant or invariant under the transformations of a compact linear group $G$ acting in a euclidean space $\real^n$, can be profitably studied as functions defined in the orbit space of the group. The orbit space is the…

This paper establishes the quantitative stability of invariant measures $\mu_{\alpha}$ for $\mathbb{R}^d$-valued ergodic stochastic differential equations driven by rotationally invariant multiplicative $\alpha$-stable processes with…