Non-degeneracy of Gauss curvature equation with negative conic singularity

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 non-degeneracy of the linearized equations.

19 pages

References in corpus (1)

• Self gravitating cosmic strings and the Alexandrov's inequality for Liouville-type equations

Cited by in corpus (2)

• A singular Sphere Covering Inequality: uniqueness and symmetry of solutions to singular Liouville-type equations
• Uniqueness of bubbling solutions of mean field equations with non-quantized singularities