#### Vol. 297, No. 2, 2018

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Nondegeneracy of the Gauss curvature equation with negative conic singularity

### Juncheng Wei and Lei Zhang

Vol. 297 (2018), No. 2, 455–475
##### Abstract

We study the Gauss curvature equation with negative singularities. For a local mean field type equation with only one negative index we prove a uniqueness property. For a global equation with one or two negative indexes we prove the nondegeneracy of the linearized equations.

##### Keywords
nondegeneracy, conic singularity, Gauss curvature, Bol's inequality
Primary: 35J75
Secondary: 58J05