A Bernstein Type Theorem for Minimal Graphs over Convex Domains

2020/08/16 by Edelen, Nick, Wang, Zhehui · 2 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2008.06815

Abstract

Given any n ≥ 2, we show that if Ω\subsetneq ℝⁿ is an open convex domain (e.g. a half-space), and u : Ω→ ℝ is a solution to the minimal surface equation which agrees with a linear function on ∂ Ω, then u must itself be linear.

Cited by

• Uniqueness in the Plateau problem for calibrated currents
• Half-space Liouville-type theorems for minimal graphs with capillary boundary

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