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Existence proofs for rotationally symmetric translating solutions to mean curvature flow

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2026

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https://doi.org/10.1016/j.difgeo.2025.102327
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http://arxiv.org/abs/2505.16688

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Differential Geometry and its Applications. 2026, 102, 102327. ISSN 0926-2245. eISSN 1872-6984. Verfügbar unter: doi: 10.1016/j.difgeo.2025.102327

Zusammenfassung

There exist rotationally symmetric translating solutions to mean curvature flow that can be written as a graph over Euclidean space. This result is well-known. Its proof uses the symmetry and techniques from partial differential equations. However, the result can also be formulated as an existence result for a singular ordinary differential equation. Here, we provide different methods to prove existence of these solutions based on the study of the singular ordinary differential equation without using methods from partial differential equations.

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510 Mathematik

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ISO 690RAJI, Hakar, Oliver C. SCHNÜRER, 2026. Existence proofs for rotationally symmetric translating solutions to mean curvature flow. In: Differential Geometry and its Applications. 2026, 102, 102327. ISSN 0926-2245. eISSN 1872-6984. Verfügbar unter: doi: 10.1016/j.difgeo.2025.102327
BibTex
@article{Raji2026Exist-75450,
  title={Existence proofs for rotationally symmetric translating solutions to mean curvature flow},
  year={2026},
  doi={10.1016/j.difgeo.2025.102327},
  volume={102},
  issn={0926-2245},
  journal={Differential Geometry and its Applications},
  author={Raji, Hakar and Schnürer, Oliver C.},
  note={Article Number: 102327}
}
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