Motion of Hypersurfaces by Gauss Curvature

@inproceedings{Andrews2000MotionOH,
  title={Motion of Hypersurfaces by Gauss Curvature},
  author={B. Andrews},
  year={2000}
}
We consider n-dimensional convex Euclidean hypersurfaces moving with normal velocity proportional to a positive power α of the Gauss curvature. We prove that hypersurfaces contract to points in finite time, and for α ∈ (1/(n + 2], 1/n] we also prove that in the limit the solutions evolve purely by homothetic contraction to the final point. We prove existence and uniqueness of solutions for non-smooth initial hypersurfaces, and develop upper and lower bounds on the speed and the curvature… CONTINUE READING

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