On the theory of minimal submanifolds and harmonic maps from the point of view of the generalized Bochner technique

2025/03/11 by С. А. Степанов, Stepanov, Sergey, Irina Tsyganok +1
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2503.08366

openalex publication_date 2025/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper, we study harmonic mappings of complete Riemannian manifolds, as well as minimal and stable minimal submanifolds of complete Riemannian manifolds. We examine classical theorems in the theory of these manifolds from the perspective of the generalized Bochner technique.

Related

• Harmonic maps from Kähler manifolds
• From harmonic mappings to Ricci flow due to the Bochner technique
• V-minimal submanifolds
• Differential geometry via harmonic functions
• The Geometry of Maximum Principles and a Bernstein Theorem in Codimension 2