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On the existence of
translating solutions of mean curvature flow in slab
regions
Theodora Bourni, Mat Langford and Giuseppe Tinaglia |
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Vol. 13 (2020), No. 4, 1051–1072
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Abstract |
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We prove, in all dimensions , that there exists a convex translator lying in a slab of width in (and in no smaller slab) if and only if . We also obtain convexity and regularity results for translators which admit appropriate symmetries and study the asymptotics and reflection symmetry of translators lying in slab regions. |
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Keywords
mean curvature flow, translators, ancient solutions
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Mathematical Subject Classification 2010
Primary: 53A10
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Milestones
Received: 12 June 2018
Revised: 3 April 2019
Accepted: 18 April 2019
Published: 13 June 2020
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Authors |
| Theodora Bourni | |
| Department of Mathematics University of Tennessee Knoxville, TN United States |
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| Mat Langford | |
| Department of Mathematics University of Tennessee Knoxville, TN United States |
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| Giuseppe Tinaglia | |
| Department of Mathematics King’s College London London United Kingdom |
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