Minimal submanifolds: Encyclopedia of Mathematical Physics

2005/11/18 by Tobias Colding, Colding, Tobias H., William P. Minicozzi +1
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.math/0511469

openalex publication_date 2005/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a quick tour through many of the classical results in the field of minimal submanifolds, starting at the definition. The field of minimal submanifolds remains extremely active and has very recently seen major developments that have solved many longstanding open problems and conjectures; for more on this, see the expanded version of this survey as well as recent surveys of Meeks and Perez, Perez, and Rosenberg.

Citations

• On the proof of the positive mass conjecture in general relativity
• Disks that are double spiral staircases
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds

Related

• Minimal submanifolds
• Singularities of minimal submanifolds
• Minimal Submanifolds of the Classical Compact Riemannian Symmetric Spaces
• New examples of higher-dimensional minimal hypersurfaces
• Lectures on Minimal Surfaces