## Kodai Mathematical Journal

- Kodai Math. J.
- Volume 35, Number 3 (2012), 523-531.

### Deforming two-dimensional graphs in *R*^{4} by forced mean curvature flow

#### Abstract

A surface Σ_{0} is a graph in *R*^{4} if there is a unit constant 2-form *w* in *R*^{4} such that ‹*e*_{1} ∧ *e*_{2}, *w*› ≥ *v*_{0} > 0, where {*e*_{1}, *e*_{2}} is an orthonormal frame on Σ_{0}. In this paper, we investigate a 2-dimensional surface Σ evolving along a mean curvature flow with a forcing term in direction of the position vector. If *v*_{0} ≥ holds on the initial graph Σ_{0} which is the immersion of the surface Σ, and the coefficient function of the forcing vector is nonnegative, then the forced mean curvature flow has a global solution, which generalizes part of the results of Chen-Li-Tian in [2].

#### Article information

**Source**

Kodai Math. J., Volume 35, Number 3 (2012), 523-531.

**Dates**

First available in Project Euclid: 15 November 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.kmj/1352985452

**Digital Object Identifier**

doi:10.2996/kmj/1352985452

**Mathematical Reviews number (MathSciNet)**

MR2997478

**Zentralblatt MATH identifier**

1257.53097

#### Citation

Mao, Jing. Deforming two-dimensional graphs in R 4 by forced mean curvature flow. Kodai Math. J. 35 (2012), no. 3, 523--531. doi:10.2996/kmj/1352985452. https://projecteuclid.org/euclid.kmj/1352985452