A note on compactness properties of the singular Toda system
Luca Battaglia, Gabriele Mancini
TL;DR
This paper investigates the blow-up behavior of solutions to the SU(3) Toda system on compact surfaces, providing a complete proof of compactness results and extending them to include singularities, aiding in solution existence proofs.
Contribution
It offers a comprehensive proof of compactness for the SU(3) Toda system and extends the results to singular cases, which was previously unestablished.
Findings
Complete proof of compactness for the SU(3) Toda system
Extension of compactness results to singular solutions
Facilitates variational methods for finding solutions
Abstract
In this note, we consider blow-up for solutions of the SU(3) Toda system on a compact surface \Sigma. In particular, we give a complete proof of the compactness result stated by Jost, Lin and Wang and we extend it to the case of singularities. This is a necessary tool to find solutions through variational methods.
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