Related papers: Gap Eigenvalues and Asymptotic Dynamics of Geometr…
We study the spatial-homogeneity of stable solutions of almost-periodic parabolic equations. It is shown that if the nonlinearity satisfies a concave or convex condition, then any linearly stable almost automorphic solution is…
We consider the Yang-Mills equations with a matrix gauge group $G$ on the de Sitter dS$_4$, anti-de Sitter AdS$_4$ and Minkowski $R^{3,1}$ spaces. On all these spaces one can introduce a doubly warped metric in the form $d s^2 =-d u^2 + f^2…
We consider the inverse problem of recovering a potential from the Dirichlet to Neumann map at a large fixed frequency on certain Riemannian manifolds. We extend the earlier result of [G. Uhlmann and Y. Wang, arXiv:2104.03477] to the case…
We present a fully pseudo-spectral scheme to solve axisymmetric hyperbolic equations of second order. With the Chebyshev polynomials as basis functions, the numerical grid is based on the Lobbato (for two spatial directions) and Radau (for…
The spectra of supergravity modes in anti de Sitter (AdS) space on a five-sphere endowed with the round metric (which is the simplest 5d Sasaki-Einstein space) has been studied in detail in the past. However for the more general class of…
We equip the whole tangent space $TM$ to a hyperbolic manifold $M$ (of constant sectional curvature -1) with a natural metric in an intrinsic way, so that the isometries of $M$ extend to isometries of $TM$ by holomorphic continuation. The…
We revisit the $k$-Hessian eigenvalue problem on a smooth, bounded, $(k-1)$-convex domain in $\mathbb R^n$. First, we obtain a spectral characterization of the $k$-Hessian eigenvalue as the infimum of the first eigenvalues of linear…
The purpose of this study is to show that the exact solutions to Yang-Mills theory can occur in two-dimensional space-time. We show that the instability of the stationary solutions for the nonabelian gauge field theories questioned by the…
We study Wave Maps from R^{2+1} to the hyperbolic plane with smooth compactly supported initial data which are close to smooth spherically symmetric ones with respect to some H^{1+\mu}, \mu>0. We show that such Wave Maps don't develop…
We give an interpretation of the global shallow water quasi-geostrophic equations on the sphere $\Sph^2$ as a geodesic equation on the central extension of the quantomorphism group on $\Sph^3$. The study includes deriving the model as a…
This work explores the possibility of obtaining a mass gap in Yang-Mills theories via the intrinsic gauge bosons, without invoking a separate Higgs boson or fermion-antifermion pairs. Instead, pairs of gauge bosons in the spin and isospin…
A large class of multidimensional nonlinear Schroedinger equations admit localized nonradial standing wave solutions that carry nonzero intrinsic angular momentum. Here we provide evidence that certain of these spinning excitations are…
We investigate the spectrum of the Dirac operator with infinite mass boundary conditions posed in a tubular neighborhood of a smooth compact hypersurface in $\mathbb{R}^n$ without boundary. We prove that when the tubular neighborhood…
We describe the $10$-dimensional space of $Sp(2)$-invariant $G_2$-structures on the homogeneous $7$-sphere $S^7=Sp(2)/Sp(1)$ as $\mathbb{R}^+\times Gl^+(3,\mathbb{R})$. In those terms, we formulate a general Ansatz for $G_2$-structures,…
We prove an inequality concerning isometries of a Gromov hyperbolic metric space, which does not require the space to be proper or geodesic. It involves the joint stable length, a hyperbolic version of the joint spectral radius, and shows…
We employ holographic duality to compute $\langle T_{\mu \nu} \rangle$ in strongly coupled $\mathcal N = 4$ supersymmetric Yang-Mills theory and then study evolution of the semiclassical Einstein field equations sourced by $\langle T_{\mu…
We construct Hadamard states for the Yang-Mills equation linearized around a smooth, space-compact background solution. We assume the spacetime is globally hyperbolic and its Cauchy surface is compact or equal $\rr^d$. We first consider the…
We introduce a class of rotationally invariant manifolds, which we call \emph{admissible}, on which the wave flow satisfies smoothing and Strichartz estimates. We deduce the global existence of equivariant wave maps from admissible…
We give the overview of solution techniques for the general conformally-invariant linear and nonlinear wave equations centered around the idea of dimensional reductions by their symmetry groups. The efficiency of these techniques is…
We investigate trend to equilibrium for the damped wave equation with a confining potential in the Euclidean space. We provide with necessary and sufficient geometric conditions for the energy to decay exponentially uniformly. The proofs…