Download this article
 Download this article For screen
For printing
Recent Issues
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
Statement, 2023
Submission guidelines
Submission form
Editorial board
ISSN (electronic): 2576-7666
ISSN (print): 2576-7658
Author index
To appear
Other MSP Journals
Harmonic metrics of generically regular semisimple Higgs bundles on noncompact Riemann surfaces

Qiongling Li and Takuro Mochizuki

Vol. 5 (2023), No. 4, 663–711

We prove that a generically regular semisimple Higgs bundle equipped with a nondegenerate symmetric pairing on any Riemann surface always has a harmonic metric compatible with the pairing. We also study the classification of such compatible harmonic metrics in the case where the Riemann surface is the complement of a finite set D in a compact Riemann surface. In particular, we prove the uniqueness of a compatible harmonic metric if the Higgs bundle is wild and regular semisimple at each point of D.

harmonic bundle, nondegenerate symmetric product, real structure
Mathematical Subject Classification
Primary: 53C07
Secondary: 58E15, 14D21, 81T13
Received: 15 October 2022
Revised: 23 July 2023
Accepted: 9 August 2023
Published: 21 November 2023
Qiongling Li
Chern Institute of Mathematics and LPMC
Nankai University
Takuro Mochizuki
Research Institute for Mathematical Sciences
Kyoto University