Prescribing sign-changing mean curvature candidates on the n+1-dimensional unit ball

2017/10/25 by Hong Zhang, Zhang, Hong
Mathematics · #35J60 #53C44 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1710.09714

openalex publication_date 2017/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper focuses on the problem of prescribing mean curvature on the unit ball. Assume that f, which is allowed to change sign, satisfies Morse index counting or certain kind of symmetry condition. By using a negative gradient flow method, we then prove that f can be realized as the boundary mean curvature of some conformal metric.

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