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
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
Authors
Juncheng Wei
Department of Mathematics
University of British Columbia
Vancouver, BC
Canada
Lei Zhang
Department of Mathematics
University of Florida
Gainesville, FL
United States