α-Mean curvature flow of non-compact complete convex hypersurfaces and the evolution of level sets
We consider the α\alpha -mean curvature flow for convex graphs in Euclidean space. Given a smooth, complete, strictly convex, non-compact initial hypersurface over a strictly convex projected domain, we derive uniform curvature bounds, which are independent of the height of a graph, to give C2{C}^{2...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2025-08-01
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| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2025-0101 |
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| Summary: | We consider the α\alpha -mean curvature flow for convex graphs in Euclidean space. Given a smooth, complete, strictly convex, non-compact initial hypersurface over a strictly convex projected domain, we derive uniform curvature bounds, which are independent of the height of a graph, to give C2{C}^{2}-estimates for convex graphs. Consequently, these height-independent estimates imply that all the derivatives for level sets converge uniformly. Furthermore, with these estimates on level sets, the boundary of the domain of a graph, which demonstrates the behavior of level sets as the height tends to infinity, is shown to be a smooth solution for the α\alpha -mean curvature flow of codimension two in the classical sense. |
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| ISSN: | 2191-950X |