Translating Solitons of the Mean Curvature Flow in Arbitrary Codimension
Translating Solitons of the Mean Curvature Flow in Arbitrary Codimension
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发表时间：
2015
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通讯作者：
Keita Kunikawa
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作者：
Keita Kunikawa
This is a survey of the Ph.D thesis by the author. In the thesis we study the translating solitons of the mean curvature flow. Although many researchers study translating solitons in codimension one, there are few references and examples for higher codimensional case. Here, we mainly consider the mean curvature flow in arbitrary codimension. Firstly, we obtain non-existence results of Bernstein type for the translating solitons in higher codimension and the eternal solutions in codimension one. Secondly we provide many new examples of translating solitons in arbitrary codimension. We will see that these examples have the property called parallel principal normal. Finally we characterize the complete translating solitons with parallel principal normal under a certain curvature condition.
