Mean curvature flow and low energy solutions of the parabolic Allen-Cahn equation on the Three-Sphere

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dc.article.number283
dc.catalogadorpva
dc.contributor.authorChen, Jingwen
dc.contributor.authorSilva Pedro Henrique, Gaspar Marques Da
dc.date.accessioned2023-06-29T15:34:53Z
dc.date.available2023-06-29T15:34:53Z
dc.date.issued2023
dc.description.abstractIn this article, we study eternal solutions to the Allen-Cahn equation in the 3-sphere, in view of the connection between the gradient flow of the associated energy functional, and the mean curvature flow. We construct eternal integral Brakke flows that connect Clifford tori to equatorial spheres, and study a family of such flows, in particular their symmetry properties. Our approach is based on the realization of Brakke’s motion by mean curvature as a singular limit of Allen-Cahn gradient flows, as studied by Ilmanen (J Differ Geom 38(2):417–461, 1993) and Tonegawa (Hiroshima Math J 33(3): 323–341, 2003), and it uses the classification of ancient gradient flows in spheres, by Choi and Mantoulidis (Amer J Math, 2019), as well as the rigidity of stationary solutions with low Morse index proved by Hiesmayr (arXiv:2007.08701 [math.DG], 2020).
dc.fechaingreso.objetodigital2023-06-29
dc.fuente.origenORCID
dc.identifier.doi10.1007/s12220-023-01347-1
dc.identifier.urihttps://doi.org/10.1007/s12220-023-01347-1
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/73996
dc.identifier.wosidWOS:001020965200001
dc.information.autorucFacultad de Matemáticas; Silva Pedro Henrique, Gaspar Marques Da; 0000-0001-8633-2601; 1250069
dc.language.isoen
dc.nota.accesoContenido parcial
dc.pagina.final30
dc.pagina.inicio1
dc.revistaThe Journal of Geometric Analysises_ES
dc.rightsacceso restringido
dc.subjectMean curvature flowes_ES
dc.subjectAllen-Cahn equationes_ES
dc.subjectPhase transitionses_ES
dc.subject.ddc510
dc.subject.deweyMatemática física y químicaes_ES
dc.titleMean curvature flow and low energy solutions of the parabolic Allen-Cahn equation on the Three-Spherees_ES
dc.typeartículo
dc.volumen33
sipa.codpersvinculados1250069
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