2018/02/10 by Shanze Gao, Hui Ma, Gao, Shanze +1
Mathematics · #53C40 #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.1802.03521
openalex publication_date 2018/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study self-similar solutions in warped products satisfying F-F=g(λ(r)∂r,ν), where F is a nonnegative constant and F is in a class of general curvature functions including powers of mean curvature and Gauss curvature. We show that slices are the only closed strictly convex self-similar solutions in the hemisphere for such F. We also obtain a similar uniqueness result in hyperbolic space ℍ3 for Gauss curvature F and F≥ 1.