| Abstract: |
| For singular mean field equations defined on a compact Riemann surface, we prove the uniqueness of bubbling solutions when blowup points are either regular points or non-quantized singular sources. In particular the uniqueness result covers the most general case extending or improving all previous works. For example, unlike previous results, we drop the assumption of singular sources being critical points of a suitably defined Kirchoff-Routh type functional. Our argument is based on refined estimates, robust and flexible enough to be applied to a wide range of problems requiring a delicate blowup analysis. In particular we come up with a major simplification of previous uniqueness proofs. Besides the uniqueness of blowup solutions, we also established the non-degeneracy of the linearized equations. This is a joint work with Daniele Bartolucci and Wen Yang. |
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