We classify the translators to the mean curvature flow in the three-dimensional solvable group Sol3 that are invariant under the action of a one-parameter group of isometries of the ambient space. In particular, we show that Sol3 admits graphical translators defined on a half plane, in contrast with a rigidity result of Shahriyari (Geom Dedicata 175:57–64, 2015) for translators in the Euclidean space. Moreover, we exhibit some nonexistence results.
Invariant translators of the solvable group
Pipoli G.
2020-01-01
Abstract
We classify the translators to the mean curvature flow in the three-dimensional solvable group Sol3 that are invariant under the action of a one-parameter group of isometries of the ambient space. In particular, we show that Sol3 admits graphical translators defined on a half plane, in contrast with a rigidity result of Shahriyari (Geom Dedicata 175:57–64, 2015) for translators in the Euclidean space. Moreover, we exhibit some nonexistence results.File in questo prodotto:
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