Ancient Mean Curvature Flows and their Spacetime Tracks
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Ancient Mean Curvature Flows and their Spacetime Tracks. / Chini, Francesco; Møller, Niels Martin.
2019. p. 1-14.Research output: Working paper › Preprint › Research
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TY - UNPB
T1 - Ancient Mean Curvature Flows and their Spacetime Tracks
AU - Chini, Francesco
AU - Møller, Niels Martin
PY - 2019
Y1 - 2019
N2 - We study properly immersed ancient solutions of the codimension one mean curvature flow in n-dimensional Euclidean space, and classify the convex hulls of the subsets of space reached by any such flow. In particular, it follows that any compact convex ancient mean curvature flow can only have a slab, a halfspace or all of space as the closure of its set of reach. The proof proceeds via a bi-halfspace theorem (also known as a wedge theorem) for ancient solutions derived from a parabolic Omori-Yau maximum principle for ancient mean curvature flows.
AB - We study properly immersed ancient solutions of the codimension one mean curvature flow in n-dimensional Euclidean space, and classify the convex hulls of the subsets of space reached by any such flow. In particular, it follows that any compact convex ancient mean curvature flow can only have a slab, a halfspace or all of space as the closure of its set of reach. The proof proceeds via a bi-halfspace theorem (also known as a wedge theorem) for ancient solutions derived from a parabolic Omori-Yau maximum principle for ancient mean curvature flows.
M3 - Preprint
T3 - arXiv.org
SP - 1
EP - 14
BT - Ancient Mean Curvature Flows and their Spacetime Tracks
ER -
ID: 311222657