Related papers: Convergence of Harder-Narasimhan polygons

This paper is devoted to the study of the stochastic-periodic homogenization of Poisson-Nernst-Planck equations in porous media. It is shown by the stochastic two-scale convergence method extended to periodic surfaces that results in a…

A well known result of Miyaoka asserts that a complex projective manifold is uniruled if its cotangent bundle restricted to a general complete intersection curve is not nef. Using the Harder-Narasimhan filtration of the tangent bundle, it…

We establish a Harder-Narasimhan formalism for modifications of $G$-bundles on the Fargues-Fontaine curve. The semi-stable stratum of the associated stratification of the $B_{dR}^+$-Grassmannian coincides with the variant of the weakly…

We introduce a notion of Gieseker stability for a filtered holomorphic vector bundle $F$ over a projective manifold. We relate it to an analytic condition in terms of hermitian metrics on $F$ coming from a construction of the Geometric…

We construct a Harder-Narasimhan filtration for rank $2$ tensors, where there does not exist any such notion a priori, as coming from a GIT notion of maximal unstability. The filtration associated to the 1-parameter subgroup of Kempf giving…

In the paper, the planar polynomial geometric interpolation of data points is revisited. Simple sufficient geometric conditions that imply the existence of the interpolant are derived in general. They require data points to be convex in a…

In this paper, we establish several new anisotropic Hardy-Sobolev inequalities in mixed Lebesgue spaces and mixed Lorentz spaces, which covers many known corresponding results. As an application, this type of inequalities allows us to…

We construct a hermitian metric on the classifying spaces of graded-polarized mixed Hodge structures and prove analogs of the strong distance estimate between an admissible period map and the approximating nilpotent orbit. We also consider…

This paper divides into two parts. Let $(X,\omega)$ be a compact Hermitian manifold. Firstly, if the Hermitian metric $\omega$ satisfies the assumption that $\partial\overline{\partial}\omega^k=0$ for all $k$, we generalize the volume of…

We expand the Chebyshev polynomials and some of its linear combination in linear combinations of the q-Hermite, the Rogers (q-utraspherical) and the Al-Salam--Chihara polynomials and vice versa. We use these expansions to obtain expansions…

Here we prove that for a smooth projective variety $X$ of arbitrary dimension and for a vector bundle $E$ over $X$, the Harder-Narasimhan filtration of a Frobenius pull back of $E$ is a refinement of the Frobenius pull-back of the…

The formalism is developed for a tree-dimensional ($3D$) nonlinear Stokes-Mueller polarimetry. The expressions are derived for the generalized $3D$ linear and nonlinear Stokes vectors, and the corresponding nonlinear Mueller matrix. The…

In this letter we numerically investigate the merging mechanism between two clusters of point vortices. We introduce a concept of renormalized Onsager function, an elaboration of the solutions of the mean field equation, and use it to…

We obtain symmetrization inequalities on probability metric spaces with convex isoperimetric profile which incorporate in their formulation the isoperimetric estimator and that can be applied to provide a unified treatment of sharp…

Given a mixed Hodge module and a meromorphic function f on a complex manifold, we associate to these data a filtration (the irregular Hodge filtration) on the exponentially twisted holonomic module, which extends the construction of…

Let L be a holomorphic line bundle over a compact complex projective Hermitian manifold X. Any fixed smooth hermitian metric h on L induces a Hilbert space structure on the space of global holomorphic sections with values in the k th tensor…

The set of diagonals of real symmetric matrices of given non negative spectrum is endowed with a measure which is obtained by the push forward of the Haar measure of the real orthogonal group.\\ We prove that the Radon Nicodym derivation of…

An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of…

By using the $\mathbb R$-filtration approach of Arakelov geometry, one establishes explicit upper bounds for geometric and arithmetic Hilbert-Samuel function for line bundles on projective varieties and hermitian line bundles on arithmetic…

Inspired by the recent work by R.Pal et al., we give further refined inequalities for a convex Riemann integrable function, applying the standard Hermite-Hadamard inequality. Our approach is different from their one in \cite{PSMA2016}. As…