Mean curvature flow and its singularity

Seminario periodico del Dipartimento di Matematica
26 aprile 2023
Orario di inizio 
PovoZero - Via Sommarive 14, Povo (Trento)
Aula seminari "1" (Povo 0)
Organizzato da: 
Dipartimento di Matematica
Comunità universitaria
Comunità studentesca UniTrento
Email per prenotazione: 
Proff. V. Agostiniani, A. Oneto, A. Pinamonti, E. Postinghel, M. Stanojkovski
Università degli Studi Trento 38123 Povo (TN) - Staff Dipartimento di Matematica
+39 04 61/281508-1625-1701-3786-1980-1511
Reto Buzano (Università degli Studi di Torino)

Abstract:  We will start this talk, which will be told mainly via pictures, with a short introduction to the mean curvature flow and the type of problems one would like to resolve with it. We will see that a major obstacle when trying to apply the flow is its singularity formation. We then discuss two results. First, we show that under some curvature assumptions the singularity formation is sufficiently simple to find ways to flow through the singularities without losing any topological information. (Here, we present joint work with Robert Haslhofer and Or Hershkovits and with Sylvain Mailot.) Second, we show that without such simplifying curvature assumptions the singularities can be arbitrarily complicated by constructing singularity models of any given genus. (This is joint work with Huy Nguyen and Mario Schulz.)

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