A Bernstein type theorem for graphic self-shrinkers with flat normal bundle

Abstract

In this note we will prove that an $n$ dimensional graphic self-shrinker in $R^{n+m}$ with flat normal bundle is a linear subspace. This result is a generalization of the corresponding result of Lu Wang in codimension one case.

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• Volume growth, eigenvalue and compactness for self-shrinkers
• On the self-shrinking systems in arbitrary codimension spaces
• Smooth compactness of self-shrinkers
• The Rigidity Theorems of Self Shrinkers via Gauss maps
• The rigidity theorems for Lagrangian self shrinkers
• Local invariants for mixed qubit-qutrit states