Cyclic Higgs bundles, subharmonic functions, and the Dirichlet problem
Differential Geometry
2023-09-26 v2 Analysis of PDEs
Complex Variables
Abstract
We demonstrate the existence and uniqueness of the solution to the Dirichlet problem for a generalization of Hitchin's equation for diagonal harmonic metrics on cyclic Higgs bundles. The generalized equations are formulated using subharmonic functions. In this generalization, the coefficient exhibits worse regularity than that in the original equation.
Keywords
Cite
@article{arxiv.2309.08465,
title = {Cyclic Higgs bundles, subharmonic functions, and the Dirichlet problem},
author = {Natsuo Miyatake},
journal= {arXiv preprint arXiv:2309.08465},
year = {2023}
}
Comments
Remarks 3, 4, and 6 have been added. Corrections related to these remarks have been made throughout the paper. 23 pages. Comments are welcome