Gradient flow for the Helfrich functional

Abstract

The author studies the L ² gradient flow of the Helfrich functional, which is a functional describing the shapes of human red blood cells. For any λ _i ≥ 0 and c ₀, the author obtains a lower bound on the lifespan of the smooth solution, which depends only on the concentration of curvature for the initial surface.

Keywords

Geometric evolution equation / Fourth order / Energy estimate

References

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