2019/10/13 by Joel Spruck, Liming Sun, Spruck, Joel +1
Mathematics · #35E10 #35J25 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Point processes and geometric inequalities #Primary: 53A10 #Secondary: 35J60 #math.AP #math.DG #msc:35E10 #msc:35J25 #msc:35J60 #msc:53A10
paper · pdf · doi:10.48550/arxiv.1910.05809
Need to fix some error in the paper. In the last step of the proof, the hypersurface of the minimal principle curvature equal to zero may be tangent to the boundary of the domain
openalex publication_date 2019/10/13 · arxiv created 2020/04/19 · arxiv updated 2020/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the Dirichlet problem for a graph Σ in ℝn+1 with normalized constant mean curvature H>0 and planar boundary Γ=∂ Ω. Our main result is that the optimal solvability condition, namely that the normalized mean curvature h of Γ satisfies h≥ H, also suffices when Ω is strictly convex, to prove the strict convexity of Σ.