Data di Pubblicazione:
2024
Citazione:
End-time regularity theorem for Brakke flows / S. Stuvard, Y. Tonegawa. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - 390:(2024 Nov), pp. 3317-3353. [10.1007/s00208-024-02826-8]
Abstract:
For a general $k$-dimensional Brakke flow in $\mathbb{R}^n$ locally close to
a $k$-dimensional plane in the sense of measure, it is proved that the flow is
represented locally as a smooth graph over the plane with estimates on all the
derivatives up to the end-time. Moreover, at any point in space-time where the
Gaussian density is close to $1$, the flow can be extended smoothly as a mean
curvature flow up to that time in a neighborhood: this extends White's local
regularity theorem to general Brakke flows. The regularity result is in fact
obtained for more general Brakke-like flows, driven by the mean curvature plus
an additional forcing term in a dimensionally sharp integrability class or in a
Hölder class.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Mean Curvature Flow; Brakke Flow; Integral Varifolds; Regularity of PDE;
Elenco autori:
S. Stuvard, Y. Tonegawa
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