Soliton solutions for the mean curvature flow
By N. Hungerbühler, Knut Smoczyk. Differential and Integral Equations, 2000
48 citations recorded by the source corpus.
We consider soliton solutions of the mean curvature flow, i.e., solutions which move under the mean curvature flow by a group of isometries of the ambient manifold. Several examples of solitons on manifolds are discussed. Moreover we present a local existence result for rotating solitons. We also prove global existence and stability for perturbed initial data close to a local soliton.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/ff45971060752d74c6258e7c424517da21d68c69
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In Applied Mathematics
- L. Alías
- J. D. de Lira
- F. Schulze
- Julie Clutterbuck
- M. Rigoli
- Robert Haslhofer
- Guofang Wang
- Chao Xia
In Astronomy and Astrophysics
In Geometry and Topology
Citations in the corpus
- Stability of translating solutions to mean curvature flow (2005, background): “For rotating “yin-yang”-curves, stability is proved in [13].”
- Mean Curvature Flow Solitons in the Presence of Conformal Vector Fields (2017, background): “However, to the best of our knowledge, there is no systematic investigation of mean curvature flow solitons in Riemannian ambient spaces in spite of some relevant contributions as, for instance, [30], [23], [32], [46].”