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arXiv · 2607.01154

Local Uniqueness and Non-degeneracy of Blow Up Solutions To A Chern-Simons System

Zetao Cheng·Haoyu Li·Lei Zhang
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Abstract

In this paper, we study blowup solutions of an important class of Chern-Simons systems. We first show that when blowup of mean-field type occurs, the corresponding blowup solution is unique under natural geometric assumptions. We also establish the non-degeneracy of the linearized system around these blowup solutions. To prove these main results, we carry out a precise blowup analysis, so that the asymptotic description of the solutions reveals the curvature information needed for the uniqueness and non-degeneracy results. Compared with related work on similar problems, our estimates are more delicate and technically involved.

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Zetao Cheng, Haoyu Li, Lei Zhang. 2026-07-01. Local Uniqueness and Non-degeneracy of Blow Up Solutions To A Chern-Simons System. https://arxiv.org/abs/2607.01154

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