2020/10/13 by Li, Qiongling, Mochizuki, Takuro · 2 citations
#53C07 #58E15 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2010.06129
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.