Modified mean curvatue flow with conic obstacle. (Flot de courbure moyenne modifiée avec obstacle conique.) (French) Zbl 1063.35096
Summary: A rotationally symmetric, compact, oriented, connected, uniformly convex hypersurface \(M_0\) of \(\mathbb R^{n+1}\), with boundary \(\partial M_0\) in a rotationally symmetric cone \(S\), is evolving under volume-preserving mean curvature flow. Then for \(n\geqslant 2\), we obtain gradient and curvature estimates, leading to long-time existence of the flow, and convergence to a part of a round sphere.
MSC:
| 35K65 | Degenerate parabolic equations |
| 53B20 | Local Riemannian geometry |
| 53B50 | Applications of local differential geometry to the sciences |
| 53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
| 35K55 | Nonlinear parabolic equations |
| 53C44 | Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010) |
Keywords:
volume-preserving mean curvature flow; gradient and curvature estimates; long-time existenceReferences:
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