On graphic Bernstein type results in higher codimension

By Mu-Tao Wang. 2002

69 citations recorded by the source corpus.

Let E be a minimal submanifold of R n+m that can be represented as the graph of a smooth map f: R n → R m . We apply a formula that we derived in the study of mean curvature flow to obtain conditions under which Σ must be an affine subspace. Our result covers all known ones in the general case. The conditions are stated in terms of the singular values of df.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/92cd9c549a425d4f4c44cc522a9425b642bcdeec

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Mao-Pei Tsui
2. L. Martinazzi
3. M. Giaquinta
4. Mu-Tao Wang
5. Knut Smoczyk
6. Matteo Cozzi

In Astronomy and Astrophysics

1. L. Martinazzi
2. M. Giaquinta
3. Mao-Pei Tsui
4. Mu-Tao Wang

In Geometry and Topology

1. L. Martinazzi
2. M. Giaquinta
3. Mao-Pei Tsui
4. Mu-Tao Wang
5. Knut Smoczyk

Citations in the corpus

• Mean curvature flows and isotopy of maps between spheres (2003, background): “Under this condition, the second author proves the Bernstein type theorem [ 21 ] and interior gradient estimates [22] for solutions of the minimal surface system.”
• An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs (2005, methodology): “In preparing this volume we particularly took advantage from the references [6] [37] [39] [52], from a series of unpublished notes by Giuseppe Modica, whom we want to thank particularly, from [98] and from the papers [109] [110] [111].”