The super-Toda system and bubbling of spinors

Jürgen Jost, Chunqin Zhou, and Miaomiao Zhu

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Submission date: 01. Sep. 2017
Pages: 31
published in: Journal of functional analysis, 276 (2019) 2, p. 410-446 
DOI number (of the published article): 10.1016/j.jfa.2018.07.002
Bibtex
Keywords and phrases: super-Toda system, blow-up, energy identity, concentration compactness
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Abstract:
We introduce the super-Toda system on Riemann surfaces and study the blow-up analysis for a sequence of solutions to the super-Toda system on a closed Riemann surface with uniformly bounded energy. In particular, we show the energy identities for the spinor parts of a blow-up sequence of solutions for which there are possibly four types of bubbling solutions, namely, finite energy solutions of the super-Liouville equation or the super-Toda system defined on ℝ² or on ℝ² ∖{0}. This is achieved by showing some new energy gap results for the spinor parts of these four types of bubbling solutions.