arXiv subjects

Ágnes Mester

Publications and source records attributed to Ágnes Mester.

10 recordsLinked to original sources

arXiv2026

Quantitative stability of extremal quasi conformal mappings

We establish quantitative stability results for classical distortion minimization problems in the theory of quasiconformal mappings. We consider the mean distortion functional and prove sharp stability estimates for the minimization problems regarding the linear stretch and spiral stretch maps, which arise as extremals in the class of mappins with finite distortion under appropriate boundary conditions. More precisely, we show that if a mapping has mean distortion close to the minimal value in the appropriate function class, then it must be quantitatively close, in certain Lebesgue norms.

math.CV↗

arXiv2026

$L^p$-Sobolev inequalities on minimal submanifolds

The paper is devoted to proving Allard-Michael-Simon-type $L^p$-Sobolev inequalities $(p>1)$ with explicit constants in the setting of Euclidean minimal submanifolds of arbitrary codimension. Our results require separate discussions for the cases $p\geq 2$ and $1<p<2$, respectively. In particular, for $p\geq 2$, we obtain an asymptotically sharp and codimension-free Sobolev constant. Our argument is based on optimal mass transport theory on Euclidean submanifolds and also provides an alternative, unified proof of the recent isoperimetric inequalities of Brendle (J. Amer. Math. Soc., 2021) and Brendle and Eichmair (Notices Amer. Math. Soc., 2024).

math.AP↗

arXiv2023

A Dirichlet inclusion problem on Finsler manifolds

In this paper we study a Dirichlet-type differential inclusion involving the Finsler-Laplace operator on a complete Finsler manifold. Depending on the positive $λ$ parameter of the inclusion, we establish non-existence, as well as existence and multiplicity results by applying non-smooth variational methods. The main difficulties are given by the problem's highly nonlinear nature due to the general Finslerian setting, as well as the nonsmooth context.

math.AP↗

arXiv2022

Sharp Morrey-Sobolev inequalities and eigenvalue problems on Riemannian-Finsler manifolds with nonnegative Ricci curvature

Combining the sharp isoperimetric inequality established by Z. Balogh and A. Kristály [Math. Ann., in press, doi:10.1007/s00208-022-02380-1] with an anisotropic symmetrization argument, we establish sharp Morrey-Sobolev inequalities on $n$-dimensional Finsler manifolds having nonnegative $n$-Ricci curvature. A byproduct of this method is a Hardy-Sobolev-type inequality in the same geometric setting. As applications, by using variational arguments, we guarantee the existence/multiplicity of solutions for certain eigenvalue problems and elliptic PDEs involving the Finsler-Laplace operator. Our results are also new in the Riemannian setting.

math.AP↗

arXiv2022

Standardized feature extraction from pairwise conflicts applied to the train rescheduling problem

We propose a train rescheduling algorithm which applies a standardized feature selection based on pairwise conflicts in order to serve as input for the reinforcement learning framework. We implement an analytical method which identifies and optimally solves every conflict arising between two trains, then we design a corresponding observation space which features the most relevant information considering these conflicts. The data obtained this way then translates to actions in the context of the reinforcement learning framework. We test our preliminary model using the evaluation metrics of the Flatland Challenge. The empirical results indicate that the suggested feature space provides meaningful observations, from which a sensible scheduling policy can be learned.

cs.LG↗

arXiv2022

Three isometrically equivalent models of the Finsler-Poincaré disk

We present the isometry between the 2-dimensional Funk model and the Finsler-Poincaré disk. Then, we introduce the Finslerian Poincaré upper half plane model, which turns out to be also isometrically equivalent to the previous models. As application, we state the gapless character of the first eigenvalue for the aforementioned three spaces.

math.DG↗

arXiv2020

Compact Sobolev embeddings on non-compact manifolds via orbit expansions of isometry groups

Given a complete non-compact Riemannian manifold $(M,g)$ with certain curvature restrictions, we introduce an expansion condition concerning a group of isometries $G$ of $(M,g)$ that characterizes the coerciveness of $G$ in the sense of Skrzypczak and Tintarev (Arch. Math., 2013). Furthermore, under these conditions, compact Sobolev-type embeddings à la Berestycki-Lions are proved for the full range of admissible parameters (Sobolev, Moser-Trudinger and Morrey). We also consider the case of non-compact Randers-type Finsler manifolds with finite reversibility constant inheriting similar embedding properties as their Riemannian companions; sharpness of such constructions are shown by means of the Funk model. As an application, a quasilinear PDE on Randers spaces is studied by using the above compact embeddings and variational arguments.

math.AP↗

arXiv2020

Sufficient criteria for obtaining Hardy inequalities on Finsler manifolds

We establish Hardy inequalities involving a weight function on complete, not necessarily reversible Finsler manifolds. We prove that the superharmonicity of the weight function provides a sufficient condition to obtain Hardy inequalities. Namely, if $ρ$ is a nonnegative function and $-\boldsymbolΔ ρ\geq 0$ in weak sense, where $\boldsymbolΔ$ is the Finsler-Laplace operator defined by $ \boldsymbolΔ ρ= \mathrm{div}(\boldsymbol{\nabla} ρ)$, then we obtain the generalization of some Riemannian Hardy inequalities given in D'Ambrosio and Dipierro (Ann. Inst. H. Poincaré, 2013). By extending the results obtained, we prove a weighted Caccioppoli-type inequality, a Gagliardo-Nirenberg inequality and a Heisenberg-Pauli-Weyl uncertainty principle on complete Finsler manifolds. Furthermore, we present some Hardy inequalities on Finsler-Hadamard manifolds with finite reversibility constant, by defining the weight function with the help of the distance function. Finally, we extend a weighted Hardy-inequality to a class of Finsler manifolds of bounded geometry.

math.DG↗

arXiv2020

A bipolar Hardy inequality on Finsler manifolds

We establish a bipolar Hardy inequality on complete, not necessarily reversible Finsler manifolds. We show that our result strongly depends on the geometry of the Finsler structure, namely on the reversibility constant $r_F$ and the uniformity constant $l_F$. Our result represents a Finslerian counterpart of the Euclidean multipolar Hardy inequality due to Cazacu and Zuazua (2013) and the Riemannian case considered by Faraci, Farkas and Kristály (2018).

math.DG↗

arXiv2019

Topological rigidity of compact manifolds supporting Sobolev-type inequalities

Let $(M,g)$ be an $n$-dimensional $(n\geq 3)$ compact Riemannian manifold with Ric$_{(M,g)}\geq (n-1)g$. If $(M,g)$ supports an AB-type critical Sobolev inequality with Sobolev constants close to the optimal ones corresponding to the standard unit sphere $(\mathbb S^n,g_0)$, we prove that $(M,g)$ is topologically close to $(\mathbb S^n,g_0)$. Moreover, the Sobolev constants on $(M,g)$ are precisely the optimal constants on the sphere $(\mathbb S^n,g_0)$ if and only if $(M,g)$ is isometric to $(\mathbb S^n,g_0)$; in particular, the latter result answers a question of V.H. Nguyen.

math.AP↗