On the Evolution of Convex Hypersurfaces by the Qk Flow
We prove the existence and uniqueness of a C1, 1 solution of the Qk flow in the viscosity sense for compact convex hypersurfaces Σt embedded in Rn+1 (n ≥ 2). The solution exists up to the time T < ∞ at which the enclosed volume becomes zero. In particular, for compact convex hypersurfaces with fl...
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| Veröffentlicht in: | Communications in partial differential equations 2010-03, Vol.35 (3), p.415 |
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| container_title | Communications in partial differential equations |
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| creator | Caputo, M Cristina Daskalopoulos, Panagiota Sesum, Natasa |
| description | We prove the existence and uniqueness of a C1, 1 solution of the Qk flow in the viscosity sense for compact convex hypersurfaces Σt embedded in Rn+1 (n ≥ 2). The solution exists up to the time T < ∞ at which the enclosed volume becomes zero. In particular, for compact convex hypersurfaces with flat sides we show that, under a certain non-degeneracy initial condition, the interface separating the flat from the strictly convex side, becomes smooth, and it moves by the Qk-1 flow at least for a short time. |
| doi_str_mv | 10.1080/03605300903296314 |
| format | Article |
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| ispartof | Communications in partial differential equations, 2010-03, Vol.35 (3), p.415 |
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| language | eng |
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| source | Taylor & Francis Journals Complete |
| subjects | Partial differential equations |
| title | On the Evolution of Convex Hypersurfaces by the Qk Flow |
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