ON THE COMPLETE 2-DIMENSIONAL λ-TRANSLATORS WITH A SECOND FUNDAMENTAL FORM OF CONSTANT LENGTH

doi:10.1007/s10473-020-0618-3

Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (6): 1897-1914.doi: 10.1007/s10473-020-0618-3

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ON THE COMPLETE 2-DIMENSIONAL λ-TRANSLATORS WITH A SECOND FUNDAMENTAL FORM OF CONSTANT LENGTH

Xingxiao LI, Ruina QIAO, Yangyang LIU

School of Mathematics and Information Sciences, Henan Normal University, Xinxiang 453007, China

Received:2019-05-24 Revised:2020-03-18 Online:2020-12-25 Published:2020-12-30
Contact: Xingxiao LI,E-mail:xxl@henannu.edu.cn E-mail:xxl@henannu.edu.cn
Supported by:
Supported by Foundation of Natural Sciences of China (11671121, 11871197 and 11971153).

Abstract

Abstract: In this article we study the two-dimensional complete $\lambda$-translators immersed in the Euclidean space $\mathbb{R}^3$ and Minkovski space $\mathbb{R}^3_1$. We obtain two classification theorems: one for two-dimensional complete $\lambda$-translators $x:M^2\to\mathbb{R}^3$ and one for two-dimensional complete space-like $\lambda$-translators $x:M^2\to\mathbb{R}^3_1$, with a second fundamental form of constant length.

Key words: singular solution, mean curvature flow, second fundamental form, λ-translator, classification

CLC Number:

53C44

Xingxiao LI, Ruina QIAO, Yangyang LIU. ON THE COMPLETE 2-DIMENSIONAL λ-TRANSLATORS WITH A SECOND FUNDAMENTAL FORM OF CONSTANT LENGTH[J].Acta mathematica scientia,Series B, 2020, 40(6): 1897-1914.

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ON THE COMPLETE 2-DIMENSIONAL λ-TRANSLATORS WITH A SECOND FUNDAMENTAL FORM OF CONSTANT LENGTH

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