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Related papers: Quasialgebraicity of Picard--Vessiot fields

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In this article uncoditional solvability of the Carleman-Vekua equation with a singular point is proved, the Riemann-Hilbert problem is solved integral representations of solutions, the strictures of their zeros and poles are recieved.

Complex Variables · Mathematics 2014-06-27 Aliaskar Tungatarov

We study algebraic isomonodromic deformations of flat logarithmic connections on the Riemann sphere with $n\geq 4$ poles, for arbitrary rank. We introduce a natural property of algebraizability for the germ of universal deformation of such…

Algebraic Geometry · Mathematics 2016-03-01 Gaël Cousin

The connected components of the zero set of any conformal vector field, in a pseudo-Riemannian manifold of arbitrary signature, are shown to be totally umbilical conifold varieties, that is, smooth submanifolds except possibly for some…

Differential Geometry · Mathematics 2011-06-07 Andrzej Derdzinski

In the framework of differential Galois theory we treat the classical spectral problem $\Psi"-u(x)\Psi=\lambda\Psi$ and its finite-gap potentials as exactly solvable in quadratures by Picard--Vessiot without involving special functions; the…

Classical Analysis and ODEs · Mathematics 2019-09-10 Yurii V. Brezhnev

Freiman's theorem gives a lower bound for the cardinality of the doubling of a finite set in $\RR^n$. In this paper we give an interpretation of his theorem for monomial ideals and their fiber cones. We call a quasi-equigenerated monomial…

Commutative Algebra · Mathematics 2018-01-17 Jürgen Herzog , Takayuki Hibi , Guangjun Zhu

We show that the non-linear autonomus Wei-Norman equations, expressing the solution of a linear system of non-autonomous equations on a Lie algebra, can be reduced to the hierarchy of matrix Riccati equations in the case of all classical…

Mathematical Physics · Physics 2013-12-19 Szymon Charzyński , Marek Kuś

In this paper we prove global existence and global behavior of solutions to quasilinear wave-Klein-Gordon systems in $\mathbb{R}^{1+2}$ with quadratic nonlinearities satisfying the null condition. We consider small, regular and compactly…

Analysis of PDEs · Mathematics 2023-12-07 Qian Zhang

We demonstrate that neutral Dirac particles in external electric fields, which are equivalent to generalized Dirac oscillators, are physical examples of quasi-exactly solvable systems. Electric field configurations permitting quasi-exact…

High Energy Physics - Theory · Physics 2015-06-26 Choon-Lin Ho , Pinaki Roy

In this note we discuss the geometry of Riemannian surfaces having a discrete set of singular points. We assume the conformal structure extends through the singularities and the curvature is integrable. Such points are called \emph{simple…

Differential Geometry · Mathematics 2022-01-11 Marc Troyanov

We show a few propositions in favour of relations between the phase space of 3D gravity, moduli of quasi-Fuchsian groups, global solutions of cosh-Gordon equations and minimal surfaces in hyperbolic spaces.

Differential Geometry · Mathematics 2008-11-21 V. V. Fock

We provide sufficient and almost optimal conditions for global existence of classical solutions in parabolic H\"older spaces to quasilinear one-dimensional parabolic problems with dynamical boundary conditions.

Analysis of PDEs · Mathematics 2015-05-04 Simon Gvelesiani , Friedrich Lippoth , Christoph Walker

A Fuchsian group $\Gamma$ has a modular embedding if its adjoint trace field is a totally real number field and every unbounded Galois conjugate $\Gamma^\sigma$ comes equipped with a holomorphic (or conjugate holomorphic) map ${\phi^\sigma…

Geometric Topology · Mathematics 2026-01-14 Matthew Stover

In this paper, we show that the global solution of the surface anisotropic two-dimensional quasi-geostrophic equation with fractional horizontal dissipation and vertical thermal diffusion established by the author in [2] is bounded in…

Analysis of PDEs · Mathematics 2022-02-15 Mustapha Amara

This dissertation is devoted to the resolution of the Plateau problem in the case of polygonal boundary curves in three-dimensional Euclidean space. It relies on the method developed by Ren\'e Garnier and published in 1928 in a paper which…

Differential Geometry · Mathematics 2011-04-01 Laura Desideri

Fuchsian methods and their applications to the study of the structure of spacetime singularities are surveyed. The existence question for spacetimes with compact Cauchy horizons is discussed. After some basic facts concerning Fuchsian…

General Relativity and Quantum Cosmology · Physics 2009-11-10 Alan D. Rendall

The paper concerns the solvability by quadratures of linear differential systems, which is one of the questions of differential Galois theory. We consider systems with regular singular points as well as those with (non-resonant) irregular…

Classical Analysis and ODEs · Mathematics 2013-12-10 Renat Gontsov , Ilya Vyugin

We formulate certain sufficient conditions for the symplectic monodromy of an isolated quasihomogeneous singularity to be of infinite order in the relative symplectic mapping class group of the Milnor fibre and give a proof using Maslov…

Differential Geometry · Mathematics 2014-04-29 Andreas Klein

Isolating cuspidal automorphic representations from the whole automorphic spectrum is a basic problem in the trace formula approach. For example, matrix coefficients of supercupidal representations can be used as test functions for this,…

Number Theory · Mathematics 2021-07-06 Li Cai , Bin Xu

We develop the theory of $\Theta$-positive representations from general Fuchsian groups to linear groups over real closed fields. Our definition, which does not assume the boundary map to be continuous, encompasses many generalizations of…

Geometric Topology · Mathematics 2026-05-25 Xenia Flamm , Nicolas Tholozan , Tianqi Wang , Tengren Zhang

\newcommand{\GLn}{\operatorname{GL}_n} \newcommand{\GL}{\GLn(C)} Let $F$ be a differential field with algebraically closed field of constants $C$. We prove that $F< Y_{ij}>(X_{ij})\supset F< Y_{ij}>$ is a generic Picard-Vessiot extension of…

Rings and Algebras · Mathematics 2007-05-23 Lourdes Juan