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Let $\Omega\subset \mathbb{R}^n $ be any open set and $u$ be a weak supersolution of $\mathcal{L}u=c(x)g(|u|)\frac{u}{|u|}$ where \[\mathcal{L}u(x)=\text{p.v.} \int_{\mathbb{R}^n} g\left(\frac{|u(x)-u(y)|}{|x-y|^s}\right)…

Let Y be an infinite covering space of a projective manifold M in P^N of dimension n geq 2. Let C be the intersection with M of at most n-1 generic hypersurfaces of degree d in P^N. The preimage X of C in Y is a connected submanifold. Let…

We study $3$-dimensional partially hyperbolic diffeomorphisms that are homotopic to the identity, focusing on the geometry and dynamics of Burago and Ivanov's center stable and center unstable \emph{branching} foliations. This extends our…

Nonlinear transport phenomena induced by chiral anomaly are explored within a 4D field theory defined holographically as $U(1)_V\times U(1)_A$ Maxwell-Chern-Simons theory in Schwarzschild-$AdS_5$. In presence of weak constant background…

We study nonequilibrium evolution in a self-interacting quantum field theory invariant under space translation only by using a canonical approach based on the recently developed Liouville-von Neumann formalism. The method is first used to…

Hosking & Schekochihin (2021, Phys. Rev. X 11, 041005) have proposed that statistically isotropic decaying MHD turbulence without net magnetic helicity conserves the mean square fluctuation level of magnetic helicity in large volumes -- or,…

In this paper we study the following class of fractional Choquard--type equations \[ (-\Delta)^{1/2}u + u=\Big( I_\mu \ast F(u)\Big)f(u), \quad x\in\mathbb{R}, \] where $(-\Delta)^{1/2}$ denotes the $1/2$--Laplacian operator, $I_{\mu}$ is…

In this paper, we develop a mini-max theory of the action functional over the semi-infinite cycles via the chain level Floer homology theory and construct spectral invariants of Hamiltonian diffeomorphisms on arbitrary, especially on {\it…

Using the fractional moment method it is shown that, within the Hartree-Fock approximation for the Disordered Hubbard Hamiltonian, weakly interacting Fermions at positive temperature exhibit localization, suitably defined as exponential…

The constraints imposed by asymptotic freedom and analyticity on the large-order behavior of perturbation theory for the electromagnetic current-current correlation function are examined. By suitably applying the renormalization group, the…

The analysis of nonlocal discrete equations driven by fractional powers of the discrete Laplacian on a mesh of size $h>0$ \[ (-\Delta_h)^su=f, \] for $u,f:\mathbb{Z}_h\to\mathbb{R}$, $0<s<1$, is performed. The pointwise nonlocal formula for…

We prove an abstract result giving a $\langle t \rangle^\varepsilon$ upper bound on the growth of the Sobolev norms of a time-dependent Schr\"odinger equation of the form ${i} \dot \psi = H_0 \psi + V (t)\psi$. Here $H_0$ is assumed to be…

In this paper we study the asymptotic behavior of $u$-capacities of small sets and its application to the analysis of the eigenvalues of the Dirichlet-Laplacian on a bounded planar domain with a small hole. More precisely, we consider two…

Starting from the hyperoctahedral multivariate hypergeometric function of Heckman and Opdam (associated with the $BC_n$ root system), we arrive -- via partial confluent limits in the sense of Oshima and Shimeno -- at solutions of the…

We consider the magnetorotational instability (MRI) of a hydrodynamically stable Taylor-Couette flow with a helical external magnetic field in the inductionless approximation defined by a zero magnetic Prandtl number ($\Pm=0)$. This leads…

This paper examines the coefficient problems for the class of semigroup generators, a topic in complex dynamics that has recently been studied in context of geometric function theory. Further, sharp bounds of coefficient functional such as…

We study the nodal set of Laplace eigenfunctions on the flat $2d$ torus $\mathbb{T}^2$. We prove an asymptotic law for the nodal length of such eigenfunctions, under some growth assumptions on their Fourier coefficients. Moreover, we show…

In this paper, we introduce and study a new class of fractional modular function spaces, called \emph{Fractional Anisotropic Musielak--Sobolev Spaces}, which generalize both the fractional Anisotropic Orlicz--Sobolev spaces and the…

The N-dimensional Hamiltonian H formed by a curved kinetic term (depending on a function f), a central potential (depending on a function U), a Dirac monopole term, and N centrifugal terms is shown to be quasi-maximally superintegrable for…

In a recent paper the first and the third authors introduced the notion of horizontal \alpha-harmonic map, with respect to a given C^1 planes distribution P_T on all R^m. The goal of this paper is to investigate compactness and quantization…