# Nonlinear asymptotic stability of homothetically shrinking Yang–Mills solitons in the equivariant case

Glogić, Irfan; Schörkhuber, Birgit

##### Abstract (englisch):
We study the heat flow for Yang-Mills connections on $\mathbb{R}^d\times SO(d)$ for $5\leq d\leq 9$. It is well-known that for this model homothetically shrinking solitons exist and an explicit example was found by Weinkove [21]. In this paper, we prove the nonlinear asymptotic stability of this solution under small $SO(d)$−equivariant perturbations and extend the results of [8] for $d=5$ to higher space dimensions. Also, we substantially simplify proof and provide new techniques to rigorously solve the spectral problem for the linearization, which turns out to be more involved in higher space dimensions.

 Zugehörige Institution(en) am KIT Institut für Analysis (IANA)Sonderforschungsbereich 1173 (SFB 1173) Publikationstyp Forschungsbericht/Preprint Publikationsjahr 2019 Sprache Englisch Identifikator ISSN: 2365-662X KITopen-ID: 1000100333 Verlag KIT, Karlsruhe Umfang 26 S. Serie CRC 1173 ; 2019/23 Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019) Externe Relationen Siehe auch Schlagwörter blowup, self-similar, geometric evolution equation, Yang-Mills, heat flow
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
KITopen Landing Page