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Structure of minimizers of the (planar) prescribed curvature functional

Giorgio Saracco
Schedule: 
Friday, October 16, 2020 - 14:00
Location: 
Online
Location: 
Zoom Meeting
Abstract: 

We will discuss some results on minimizers of the prescribed curvature functional  ${\rm Per}(E)-k|E|$ among subsets of a planar bounded set $\Omega$. We will show a geometric characterization of minimizers w.r.t. a special class of sets $\Omega$, namely those with "no necks'' of radius the inverse of the prescribed curvature $k$. As a by-product, we obtain some results for the Cheeger problem and the isoperimetric problem in those $\Omega$s.
Based on joint works with G.P. Leonardi (Università di Trento) and R. Neumayer (Northwestern University)

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