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| Gradient Flow for the Helfrich Functional |
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Citation： |
Yannan LIU.Gradient Flow for the Helfrich Functional[J].Chinese Annals of Mathematics B,2012,33(6):931~940 |
| Page view： 1693
Net amount： 1199 |
Authors： |
Yannan LIU; |
Foundation： |
the National Natural Science Foundation of China (No. 11026121) and the Training
Programme Foundation for the Excellent Talents of Beijing (No. 2012D005003000004). |
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| 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 $\lambda_{i}\geq 0$ 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 |
Classification： |
35J60, 35K45, 52K44, 53A05 |
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