Isolated singularities of Toda equations and cyclic Higgs bundles

Abstract

This paper is the second part of our study on the Toda equations and the cyclic Higgs bundles associated to $r$-differentials over non-compact Riemann surfaces. We classify all the solutions up to boundedness around the isolated singularity of an $r$-differential under the assumption that the $r$-differential is meromorphic or has some type of essential singularity. As a result, for example, we classify all the solutions on $\mathbb{C}$ if the $r$-differential is a finite sum of the exponential of polynomials.

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References in corpus (5)

• Wild Harmonic Bundles and Wild Pure Twistor D-modules
• Asymptotic behaviour of certain families of harmonic bundles on Riemann surfaces
• G2 geometry and integrable systems
• Planar minimal surfaces with polynomial growth in the $\mathrm{Sp}(4,\mathbb{R})$-symmetric space
• Complete solutions of Toda equations and cyclic Higgs bundles over non-compact surfaces

Cited by in corpus (1)

• Complete solutions of Toda equations and cyclic Higgs bundles over non-compact surfaces