Gaussian curvature of minimal graphs in M× ℝ

2022/07/11 by David Kalaj, Kalaj, David
Biochemistry, Genetics and Molecular Biology · Mathematics · #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Myofascial pain diagnosis and treatment

paper · pdf · doi:10.48550/arxiv.2207.04769

openalex publication_date 2022/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider minimal graphs in the three-dimensional Riemannian manifold M×ℝ. We mainly estimate the Gaussian curvature of such surfaces. We consider the minimal disks and minimal graphs bounded by two Jordan curves in parallel planes. The key to the proofs is the Weierstrass representation of those surfaces via \wp-harmonic mappings. We also prove some Schwarz lemma type results and some Heinz type results for harmonic mappings between geodesic disks in Riemannian surfaces.

Related

• Gaussian curvature conjecture for minimal graphs
• Curvature of minimal graphs
• On a sharp form of curvature conjecture for minimal graphs
• A note on two-dimensional minimal surface graphs in Rⁿ and a theorem of Bernstein-Liouville type
• An estimate for the Gauss curvature of minimal surfaces in \mathbb R^m whose Gauss map omits a set of hyperplanes