Details

Autor(en) / Beteiligte

• Sauvigny, Friedrich

Titel

Minimal graphs in Riemannian spaces

Ist Teil von

• Calculus of variations and partial differential equations, 2024-06, Vol.63 (5)

Ort / Verlag

Berlin/Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2024

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• In this treatise, we discuss existence and uniqueness questions for parametric minimal surfaces in Riemannian spaces, which represent minimal graphs. We choose the Riemannian metric suitably such that the variational solution of the Riemannian Dirichlet integral under Dirichlet boundary conditions possesses a one-to-one projection onto a plane. At first we concentrate our considerations on existence results for boundary value problems. Then we study uniqueness questions for boundary value problems and for complete minimal graphs. Here we establish curvature estimates for minimal graphs on discs, which imply Bernstein-type results.