[HTML][HTML] Graph-to-local limit for the nonlocal interaction equation

A Esposito, G Heinze, A Schlichting - Journal de Mathématiques Pures et …, 2025 - Elsevier
We study a class of nonlocal partial differential equations presenting a tensor-mobility, in
space, obtained asymptotically from nonlocal dynamics on localising infinite graphs. Our …

An asymmetric arzela–ascoli theorem

J Collins, J Zimmer - Topology and its Applications, 2007 - Elsevier
An asymmetric Arzelà–Ascoli theorem Page 1 Topology and its Applications 154 (2007)
2312–2322 www.elsevier.com/locate/topol An asymmetric Arzelà–Ascoli theorem Julia …

Nonlocal cross-interaction systems on graphs: Nonquadratic Finslerian structure and nonlinear mobilities

G Heinze, JF Pietschmann, M Schmidtchen - SIAM Journal on Mathematical …, 2023 - SIAM
We study the evolution of a system of two species with nonlinear mobility and nonlocal
interactions on a graph whose vertices are given by an arbitrary, positive measure. To this …

Gradient flows in asymmetric metric spaces and applications

S Ohta, W Zhao - arxiv preprint arxiv:2206.07591, 2022 - arxiv.org
This paper is devoted to the investigation of gradient flows in asymmetric metric spaces (for
example, irreversible Finsler manifolds and Minkowski normed spaces) by means of discrete …

Asymmetric Geometry of Total Grassmannians

ALG Mandolesi - arxiv preprint arxiv:2310.17865, 2023 - arxiv.org
Metrics in Grassmannians, or distances between subspaces of same dimension, have many
applications. However, usual extensions to the Total Grassmannian of subspaces of different …

[HTML][HTML] Almost isometries of non-reversible metrics with applications to stationary spacetimes

MA Javaloyes, L Lichtenfelz, P Piccione - Journal of Geometry and Physics, 2015 - Elsevier
We develop the basics of a theory of almost isometries for spaces endowed with a quasi-
metric. The case of non-reversible Finsler (more specifically, Randers) metrics is of particular …

Young measure flow as a model for damage

MO Rieger, J Zimmer - Zeitschrift für angewandte Mathematik und Physik, 2009 - Springer
Models for hysteresis in continuum mechanics are studied that rely on a time-discretised
quasi-static evolution of Young measures akin to a gradient flow. The main feature of this …

On tight spans for directed distances

H Hirai, S Koichi - Annals of Combinatorics, 2012 - Springer
An extension (V, d) of a metric space (S, μ) is a metric space with S ⊆ V and d ∣ _S= μ, and
is said to be tight if there is no other extension (V, d′) of (S, μ) with d′≤ d. Isbell and Dress …

Gradient flows of time-dependent functionals in metric spaces and applications to PDEs

LCF Ferreira, JC Valencia-Guevara - Monatshefte für Mathematik, 2018 - Springer
We develop a gradient-flow theory for time-dependent functionals defined in abstract metric
spaces. Global well-posedness and asymptotic behavior of solutions are provided …

Asymmetric metrics on the full Grassmannian of subspaces of different dimensions

ALG Mandolesi - arxiv preprint arxiv:2208.05026, 2022 - arxiv.org
Metrics on Grassmannians have a wide array of applications: machine learning, wireless
communication, computer vision, etc. But the available distances between subspaces of …