Related papers: Quasialgebraicity of Picard--Vessiot fields

In this paper we study quasilinear elliptic systems with nonlinear boundary condition with fully coupled perturbations even on the boundary. Under very general assumptions our main result says that each weak solution of such systems belongs…

We revisit the propagation of classical scalar fields in a spacetime which is asymptotically anti-de Sitter. The lack of global hyperbolicity of the underlying background gives rise to an ambiguity in the dynamical evolution of solutions of…

In this note, we give explicit expressions of Gauss sums for general (resp. special) linear groups over finite fields, which involves Gauss sums (resp. Kloosterman sums). The key ingredient is averaging such sums over Borel subgroups. As…

The main objective of the present work is to discuss the global existence and stability of solutions to the porous medium equations on Riemannian manifolds with singularities. Several different types of solutions are considered. Our proof…

We classify the allowed structures of the discrete 1-form gauge sector in six-dimensional supergravity theories realized as F-theory compactifications. This provides upper bounds on the 1-form gauge factors $\mathbb{Z}_m$ and in particular…

We review the application of the spectral zeta-function to the 1- loop properties of quantum field theories on manifolds with boundary, with emphasis on Euclidean quantum gravity and quantum cosmology. As was shown in the literature some…

For specifically coupled values of the quadratic gravity parameters, we present a fully explicit static spherically symmetric solution. It contains the central singularity surrounded by the black-hole or the cosmological horizon for the…

We derive a necessary and sufficient condition for Poincar\'e Lie superalgebras in any dimension and signature to be isomorphic. This reduces the classification problem, up to certain discrete operations, to classifying the orbits of the…

We show that a group admits a non-zero homogeneous quasimorphism if and only if it admits a certain type of action on a poset. Our proof is based on a construction of quasimorphisms which generalizes Poincar\'e--Ghys' construction of the…

Let S be a compact surface of genus >1, and g be a metric on S of constant curvature K\in\{-1,0,1\} with conical singularities of negative singular curvature. When K=1 we add the condition that the lengths of the contractible geodesics are…

Global stability of the spherically symmetric nonisentropic compressible Euler equations with positive density around global-in-time background affine solutions is shown in the presence of free vacuum boundaries. Vacuum is achieved despite…

In this paper, we prove existence and regularity of positive solutions for singular quasilinear elliptic systems involving gradient terms. Our approach is based on comparison properties, a priori estimates and Schauder's fixed point…

We use Fuchsian Reduction to study the behavior near the singularity of a class of solutions of Einstein's vacuum equations. These solutions admit two commuting spacelike Killing fields like the Gowdy spacetimes, but their twist does not…

We present some sufficient conditions for the global in time existence of solutions of the semilinear Klein-Gordon equation of the self-interacting scalar field with complex mass. The coefficients of the equation depend on spatial variables…

We study plane quadratic and cubic differential systems satisfying the Caushy - Riemann conditions. We construct all global topologically equivalent phase portraits of the systems.

We prove that the holomorphic solutions of Picard-Fuchs differential equations associated with one-parameter families of abelian varieties with real multiplication admit power series expansions with $S$-integral coefficients at a maximal…

In an earlier paper it was proved that if a differential field $(K,\delta)$ is algebraically closed and closed under Picard-Vessiot extensions then every differential algebraic principal homogeneous space over K for a linear differential…

We prove existence of global solutions to singular SPDEs on $\mathbb{R}^d$ with cubic nonlinearities and additive white noise perturbation, both in the elliptic setting in dimensions $d=4,5$ and in the parabolic setting for $d=2,3$. We…

Let G be a compact Lie group acting transitively on Riemannian manifolds M and N. Let p be a G equivariant Riemannian submersion from M to N. We show that a smooth differential form on N has finite Fourier series if and only if the pull…

We study a general field theory of a scalar field coupled to gravitation through a quadratic Gauss-Bonnet term $\xi({\phi})$$R_{GB}^2$. We show that, under mild assumptions about the function $\xi(\phi)$, the classical solutions in a…