Nondegeneracy of the Gauss curvature equation with negative conic singularity

Juncheng Wei and Lei Zhang

Vol. 297 (2018), No. 2, 455–475

DOI: 10.2140/pjm.2018.297.455

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

Mathematical Subject Classification 2010

Primary: 35J75

Secondary: 58J05

Milestones

Received: 17 July 2017

Revised: 9 April 2018

Accepted: 10 April 2018

Published: 20 December 2018