Kodai Mathematical Journal

Deforming two-dimensional graphs in R4 by forced mean curvature flow

Jing Mao

Full-text: Open access

Abstract

A surface Σ0 is a graph in R4 if there is a unit constant 2-form w in R4 such that ‹e1e2, w› ≥ v0 > 0, where {e1, e2} is an orthonormal frame on Σ0. 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 v0${1 \over \sqrt {2}}$ holds on the initial graph Σ0 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


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