Bubbles with constant mean curvature, and almost constant mean curvature, in the hyperbolic space

2020/08/07 by Gabriele Cora, Cora, G., Roberta Musina +1
Mathematics · #35R01 #53A10 #53C21 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2008.03227

openalex publication_date 2020/08/07 · openalex created_date 2020/08/13 · openalex updated_date 2026/07/28

Abstract

Given a constant k>1, let Z be the family of round spheres of radius \textrmartanh(k^-1) in the hyperbolic space ℍ³, so that any sphere in Z has mean curvature k. We prove a crucial nondegeneracy result involving the manifold Z. As an application, we provide sufficient conditions on a prescribed function ϕ on ℍ³, which ensure the existence of a \cal C¹-curve, parametrized by ε≈ 0, of embedded spheres in ℍ³ having mean curvature k +εϕ at each point.

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