Gradient Estimates of Mean Curvature Equation with Neumann Boundary Condition in Mⁿ× ℝ

2016/06/21 by Jinju Xu, Xu, Jinju, Dekai Zhang +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1606.06569

openalex publication_date 2016/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we study the prescribed mean curvature equation with Neumann boundary conditions on Riemannian product manifold Mⁿ× ℝ. The main goal is to establish the boundary gradient estimates for solutions by the maximum principle. As a consequence, we obtain an existence result.

Citations

• On capillary free surfaces in a gravitational field

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