Communications in Analysis and Geometry

Volume 22 (2014)

Number 5

Spacelike self-similar shrinking solutions of the mean curvature flow in pseudo-Euclidean spaces

Pages: 897 – 929

DOI: http://dx.doi.org/10.4310/CAG.2014.v22.n5.a6

Author

Márcio Adames Rostirolla (Departamento Acadêmico de Matemática, UTFPR, Curitiba, Brazil)

Abstract

I classify spacelike self-similar shrinking solutions of the mean curvature flow in pseudo-Euclidean space in arbitrary codimension, if the mean curvature vector is not a null vector and the principal normal vector is parallel in the normal bundle. Moreover, I exclude the existence of such self-shrinkers in several cases. The classification is analogous to the existing classification in the Euclidean case.

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