Inverse mean curvature flow inside a cone in warped products. arXiv:1705.04865
Preprint, arXiv:1705.04865 [math.DG] (2017).
Summary: Given a convex cone in the prescribed warped product, we consider hypersurfaces with boundary which are star-shaped with respect to the center of the cone and which meet the cone perpendicularly. If those hypersurfaces inside the cone evolve along the inverse mean curvature flow, then, by using the convexity of the cone, we can prove that this evolution exists for all the time and the evolving hypersurfaces converge smoothly to a piece of round sphere as time tends to infinity.
MSC:
| 53C44 | Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010) |
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
| 35B45 | A priori estimates in context of PDEs |
| 35K93 | Quasilinear parabolic equations with mean curvature operator |
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