A Bernstein-type theorem for -submanifolds with flat normal bundle in the Euclidean spaces

DOI10.3906/MAT-1710-1zbMath1412.53012OpenAlexW2908564370WikidataQ128537214 ScholiaQ128537214MaRDI QIDQ5742909

Peibiao Zhao, Xuyong Jiang, He Jun Sun

Publication date: 8 May 2019

Published in: TURKISH JOURNAL OF MATHEMATICS (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3906/mat-1710-1

zbMATH Keywords

Bernstein-type theorem\(\xi\)-submanifold

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (1)

A Bernstein type theorem for entire graphic 2-dimensional \(\Lambda \)-submanifolds in \(\mathbf{R}^4 \)

Cites Work

• Volume growth eigenvalue and compactness for self-shrinkers
• Generic mean curvature flow. I: Generic singularities
• The hyperplane is the only stable, smooth solution to the isoperimetric problem in Gaussian space
• Variational characterizations of \(\xi\)-submanifolds in the Eulicdean space \(\mathbb{R}^{m+p}\)
• Curvature estimates for minimal hypersurfaces
• Non-existence, non-uniqueness and irregularity of solutions to the minimal surface system
• Complete \(\lambda \)-hypersurfaces of weighted volume-preserving mean curvature flow
• Bernstein type theorems for higher codimension
• A Bernstein type theorem for self-similar shrinkers
• Bernstein type theorems with flat normal bundle
• A rigidity theorem of \(\xi \)-submanifolds in \({\mathbb {C}}^{2}\)
• Minimal varieties in Riemannian manifolds
• Submanifolds with finite type Gauss map
• Volume estimate about shrinkers

This page was built for publication: A Bernstein-type theorem for -submanifolds with flat normal bundle in the Euclidean spaces