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# Communications in Analysis and Geometry

## Volume 11 (2003)

### Number 4

### Evolution of radial graphs in hyperbolic space by their mean curvature

Pages: 675 – 698

DOI: http://dx.doi.org/10.4310/CAG.2003.v11.n4.a2

#### Author

#### Abstract

We consider the evolution of a surface **F** : *M*^{n} ↦ ℋ^{n+1} in hyperbolic space by mean curvature flow. That is, we study the one parameter family **F**_{t} = **F**(., *t*) of immersions with corresponding images *M*_{t} = **F** _{t} (*M*^{n}) such that

δ / δ*t* **F**(*p, t*) =ℋ(*p, t*), *p* ∈ *M*^{n}

**F**(*p,* 0) = **F**_{0}(*p*)

where ℋ(*p, t*) is the mean curvature vector of the hypersurface M_{t} at **F**(*p, t*) in hyperbolic space.