[CvGmt News] Seminario Langford 14/7/2016

[Alfonso Sorrentino]

SEMINARIO DI ANALISI ED EQUAZIONI DIFFERENZIALI
Dipartimento di Matematica
Università degli Studi di Roma "Tor Vergata"


Giovedì 14 luglio, ore 14:30, Aula Dal Passo

Mat Langford (Freie Universität, Berlin)

Title: Slowly forming singularities of the mean curvature flow

Abstract: We will consider translating solutions of the mean curvature flow
(or translators for short); that is, solutions of the mean curvature flow
which evolve purely by translation. Strictly convex translators are of
particular interest, as they arise as `blow-up limits' of singularities of
mean convex mean curvature flow. It was a longstanding conjecture that
strictly convex translators should be rotationally symmetric. This was
famously proved, by X. J. Wang, to be true in two space dimensions, but
false in all higher dimensions; however, the question remained open for
translators which arise as blow-ups of singularities. It was recently proved
by Haslhofer that two-convex, non-collapsing translating solutions are
necessarily rotationally symmetric. It then follows from a result of Andrews
that any translator which arises as a blow-up limit of a two-convex embedded
mean curvature flow is necessarily rotationally symmetric. We will show how
to remove the non-collapsing assumption in spatial dimensions $n\geq 3$ by
instead making use of estimates of Huisken and Sinestrari. As a consequence,
we deduce that any translator which arises as a blow-up limit of a
two-convex immersed mean curvature flow is necessarily rotationally
symmetric.


Website: http://www.mat.uniroma2.it/~castorin/Seminario-PDE.html



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Email: sorrentino at mat.uniroma2.it