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2022•Mediterranean Journal of MathematicsOpen access

Translating Solitons in a Lorentzian Setting, Submersions and Cohomogeneity One Actions

Marie-Amélie Lawn, Miguel Ortega

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Abstract

Abstract We study new examples of translating solitons of the mean curvature flow, especially in Minkowski space. We consider for this purpose manifolds admitting submersions and cohomegeneity one actions by isometries on suitable open subsets. This general setting also covers the classical Euclidean examples. As an application, we completely classify time-like, invariant translating solitons by rotations and boosts in Minkowski space.

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Abstract We study new examples of translating solitons of the mean curvature flow, especially in Minkowski space. We consider for this purpose manifolds admitting submersions and cohomegeneity one actions by isometries on suitable open subsets. This general setting also covers the classical Euclidean examples. As an application, we completely classify time-like, invariant translating solitons by rotations and boosts in Minkowski space.

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Available abstract

Abstract We study new examples of translating solitons of the mean curvature flow, especially in Minkowski space. We consider for this purpose manifolds admitting submersions and cohomegeneity one actions by isometries on suitable open subsets. This general setting also covers the classical Euclidean examples. As an application, we completely classify time-like, invariant translating solitons by rotations and boosts in Minkowski space.

Key concepts: Minkowski space, Mathematics, Pure mathematics, Euclidean geometry, Invariant (physics), Euclidean space, Space (punctuation), Curvature

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