Niels Martin Møller University of Copenhagen

(Non)uniqueness of tangent planes and removable singularities at infinite time for the translating solitons equation

Abstract:

Translating solitons for mean curvature flow are, in certain collapsed cases, known to subconverge locally to "tangent planes at infinity", as time t → ±∞. This raises the natural question whether L^∞ solutions to the quasilinear equation with a drift term may at large scales "wobble" off towards infinity, or if there hold removable singularities theorems at infinite times?

The question turns out to yield a delicate "yes and no": Yes, as we will in this talk prove, for complete solitons, such tangent planes are indeed uniquely defined (with geometric consequences in the classification program). No, as we construct solitons complete with boundary which, despite decay of all derivatives, admit a continuum of vertical planes as subsequential limits.

(Joint work with E.S. Gama and F. Martín.)