2022/01/19 by Antonio Bueno, Bueno, Antonio, Irene Ortiz +1
Mathematics · Physics and Astronomy · #34C05 #34C40 #53A10 #53C42 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2201.07480
openalex publication_date 2022/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a,b∈ℝ and Φ∈ C1(\mathbbS2), we study immersed oriented surfaces Σ in the Euclidean 3-space ℝ3 whose mean curvature H and Gauss curvature K satisfy 2aH+bK=Φ(N), where N:Σ→\mathbbS2 is the Gauss map. This theory widely generalize some of paramount importance such as the ones constant mean and Gauss curvature surfaces, linear Weingarten surfaces and self-translating solitons of the mean curvature flow. Under mild assumptions on the prescribed function Φ, we exhibit a classification result for rotational surfaces in the case that the underlying fully nonlinear PDE that governs these surfaces is elliptic or hyperbolic.