Related papers: Stable Flags and the Riemann-Hilbert Problem

Let $X_\lambda^\mu := X_\lambda \cap X^\mu \subseteq G/P$ be a Richardson variety in a generalized partial flag manifold. We use equivariant stable map spaces to define a canonical resolution $\widetilde{X_\lambda^\mu}$ of singularities,…

We study the Ginzburg-Landau equations on Riemann surfaces of arbitrary genus. In particular: - we construct explicitly the (local moduli space of gauge-equivalent) solutions in a neighbourhood of the constant curvature ones; - classify…

Let $(E,\overline{\partial}_E,\theta)$ be a stable Higgs bundle of degree $0$ on a compact connected Riemann surface. Once we fix the flat metric $h_{\det(E)}$ on the determinant of $E$, we have the harmonic metrics $h_t$ $(t>0)$ for the…

A localisation of the category of n-manifolds is introduced by formally inverting the connected sum construction with a chosen n-manifold Y. On the level of automorphism groups, this leads to the stable diffeomorphism groups of n-manifolds.…

This paper focuses on the analysis of stratified steady periodic water waves that contain stagnation points. The initial step involves transforming the free-boundary problem into a quasilinear pseudodifferential equation through a conformal…

We show that the "eigenbundle" (localization bundle) of certain Hilbert modules over bounded symmetric domains of rank r is a "singular" vector bundle (linearly fibrered complex analytic space) which decomposes as a stratified sum of…

A fast and accurate numerical method for the solution of scalar and matrix Wiener--Hopf problems is presented. The Wiener--Hopf problems are formulated as Riemann--Hilbert problems on the real line, and a numerical approach developed for…

Fix a simple complex Lie group G and a principal sl(2,C) subalgebra of Lie(G). Then the moduli space of semi-stable, topologically trivial G-Higgs bundles on a hyperbolic, spin Riemann surface acquires a marked point. This is the unique…

The purpose of these notes is to show that the methods introduced by Bauer and Furuta in order to refine the Seiberg-Witten invariants of smooth 4-dimensional manifolds can also be used to obtain stable homotopy classes from Riemann…

This is an extensive survey of the techniques used to formulate generalizations of the Mittag-Leffler Theorem from complex analysis. With the techniques of the theory of differential forms, sheaves and cohomology, we are able to define the…

A 2D problem of acoustic wave scattering by a segment bearing impedance boundary conditions is considered. In the current paper (the first part of a series of two) some preliminary steps are made, namely, the diffraction problem is reduced…

In this note, we show that the solution to the Dirichlet problem for the minimal surface system in any codimension is unique in the space of distance-decreasing maps. This follows as a corollary of the following stability theorem: if a…

In the literature, there are two standard rank filtrations on $K$-theory: an ``unstable'' one which is traditionally defined through the homology of $GL_n$, and a ``stable'' one which was defined by Rognes using the simplicial structure on…

We consider stability and approximate reconstruction of Riemannian manifold when the finite number of eigenvalues of the Laplace-Beltrami operator and the boundary values of the corresponding eigenfunctions are given. The reconstruction can…

In this paper, we study geometric rigidity of Riemannian manifolds admitting stable solutions of certain elliptic problems (stability in a variational sense), that is, under suitable hypotheses, we are able to characterize the Riemannian…

An important classification problem in Algebraic Geometry deals with pairs $(\E,\phi)$, consisting of a torsion free sheaf $\E$ and a non-trivial homomorphism $\phi\colon (\E^{\otimes a})^{\oplus b}\lra\det(\E)^{\otimes c}\otimes \L$ on a…

The problem of reconstruction of an unknown refractive index $k(x)$ of an inhomogeneous solid $P$ is considered. The refractive index is assumed to be a piecewise-H\"{o}lder function The original boundary value problem for the Helmholtz…

I show that the cohomology of the generic points of algebraic complex varieties becomes {\sl stable} birational invariant, when considered `modulo the cohomology of the generic points of the affine spaces'.

We investigate the stability and long-term behavior of spatially periodic plane waves in the complex Klein-Gordon equation under localized perturbations. Such perturbations render the wave neither localized nor periodic, placing its…

We consider the Riemann problem of the dilute approximation equations with spatiotemporally dependent volume fractions from the full model of suspension, in which the particles settle to the solid substrate and the clear liquid film flows…