NDLI: Bernstein-type theorem of translating solitons in arbitrary codimension with flat normal bundle

Content Provider	Springer Nature Link
Author	Kunikawa, Keita
Copyright Year	2015
Abstract	We give a proof for a Bernstein-type theorem of complete graphs of translating solitons in higher codimension. In the case of hypersurfaces, Bao–Shi showed that a translating soliton whose image of the Gauss map is contained in a compact subset in an open hemisphere is a hyperplane. This means that there is no nontrivial translating soliton whose slope is bounded. In the present article, we generalize this theorem in arbitrary codimension. Moreover we obtain an optimal growth condition which allows unbounded slopes. As a corollary, our result covers a classical Bernstein-type theorem for minimal submanifolds.
Ending Page	1344
Page Count	14
Starting Page	1331
File Format	PDF
ISSN	09442669
e-ISSN	14320835
Journal	Calculus of Variations and Partial Differential Equations
Issue Number	2
Volume Number	54
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2015-01-28
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Immersions (minimal, prescribed curvature, tight, etc.) Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Analysis Theoretical, Mathematical and Computational Physics Higher-dimensional and -codimensional surfaces in Euclidean $n$ -space Special Riemannian manifolds (Einstein, Sasakian, etc.)
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis

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Bernstein-type theorem of translating solitons in arbitrary codimension with flat normal bundle