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

TL;DR

This paper proves that n-dimensional graphic self-shrinkers with flat normal bundles in Euclidean space are necessarily linear subspaces, extending previous results from codimension one to higher codimensions.

Contribution

It generalizes Lu Wang's codimension one result to higher codimensions, establishing a Bernstein type theorem for graphic self-shrinkers with flat normal bundles.

Findings

Graphic self-shrinkers with flat normal bundle are linear subspaces.

Extension of Bernstein type theorem to higher codimension.

Provides a characterization of self-shrinkers under flat normal bundle condition.

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.