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We consider the mean curvature flow of a closed hypersurface in hyperbolic space. Under a suitable pinching assumption on the initial data, we prove a priori estimate on the principal… Click to show full abstract
We consider the mean curvature flow of a closed hypersurface in hyperbolic space. Under a suitable pinching assumption on the initial data, we prove a priori estimate on the principal curvatures which implies that the asymptotic profile near a singularity is either strictly convex or cylindrical. This result generalizes the estimates obtained in the previous works of Huisken, Sinestrari and Nguyen on the mean curvature flow of hypersurfaces in Euclidean spaces and in the spheres.
Keywords:
estimates mean;
cylindrical estimates;
curvature flow;
mean curvature
Journal Title: Communications on Pure and Applied Analysis
Year Published: 2021
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Journal Title: Communications on Pure and Applied Analysis
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!