Weak asymptotical stability of Yang-Mills' gradient flow
type: Item
instance of: scholarly article
title: Weak asymptotical stability of Yang-Mills' gradient flow
zbMATH Open document ID: 0691.58033
author: Kazuyo Kono
author: Takeyuki Nagasawa
published in: Tokyo Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: The authors study the Yang-Mills functional \(J(\nabla)\) which is given by the square integral of the curvature associated to a metric connection \(\nabla\) on a Riemannian vector bundle E over a Riemannian manifold M. For the case where M is the Euclidean space \(R^ n\) or a bounded domain in \(R^ n\) with smooth boundary \((n\geq 2)\) and E is the trivial vector bundle they prove the asymptotical stability of the canonical flat connection of E (a critical point of the Yang-Mills functional) in certain function space for the gradient flow \(\nabla(t)\) satisfying the equation \(\frac{d\nabla(t)}{dt}=-\text{grad} J(\nabla(t))\). Special gauge conditions are assumed.
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 58E99
zbMATH DE Number: 4131317
zbMATH Keywords: Yang-Mills flow
zbMATH Keywords: Yang-Mills functional
zbMATH Keywords: asymptotical stability
reviewed by: Yuri E. Gliklikh
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270133980
OpenAlex ID: W2026994654
DOI: 10.3836/TJM/1270133980
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description: scientific article; zbMATH DE number 4131317