Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.00036 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- In this note, we study the singular mean field equation defined on a Riemann surface with a sign-changing potential function. We prove if some singular sources happen to be placed on the zero-level curve of the potential function, a priori estimate can still be obtained. As a consequence of this estimate, existence and multiplicity results can still be obtained based on the topology of the manifold.