Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2505.17892 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Inhaltsangabe:
- In this work we study the existence of solutions to the Mean Curvature Flow for which the initial condition has the structure of a two-dimensional Lie subgroup within a Lie group of dimension three. We consider Lie groups with a fixed left-invariant metric and first observe that if the Lie group is unimodular, then every Lie subgroup is a minimal surface (hence a trivial solution). For this reason we focus on non-unimodular Lie groups, finding the evolution of every Lie subgroup of dimension 2 (within a 3 dimensional Lie group). These evolutions are self-similar for abelian subgroups (i.e. evolve by isometries), but not self-similar in the other cases.