Complete Self-Shrinking Solutions for Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space
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Letf(x)be a smooth strictly convex solution ofdet(∂2f/∂xi∂xj)=exp(1/2)∑i=1nxi(∂f/∂xi)-fdefined on a domainΩ⊂Rn; then the graphM∇fof∇fis a space-like self-shrinker of mean curvature flow in Pseudo-Euclidean spaceRn2nwith the indefinite metric∑dxidyi. In this paper, we prove a Bernstein theorem for complete self-shrinkers. As a corollary, we obtain if the Lagrangian graphM∇fis complete inRn2nand passes through the origin then it is flat.
2020 ◽
Vol 148
(10)
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pp. 4557-4571
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2009 ◽
Vol 243
(2)
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pp. 331-355
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2009 ◽
Vol 13
(1)
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pp. 89-100
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2011 ◽
Vol 32
(2)
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pp. 187-200
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2018 ◽
Vol 274
(1)
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pp. 252-277
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