28 feb 2025 -- 10:00   [open in google calendar]

Centro de Giorgi, Sala Conferenze

Abstract.

In the seminal paper of 1995, J. C. C. Nitsche proved that if a domain of R³ is uniformly dense in its boundary, then the boundary has to be a plane or a right helicoid, closing an open problem proposed by G. Cimmino in 1932. This result has since inspired a rich line of research on rigidity phenomena for overdetermined differential problems in possibly unbounded domains. The aim of this talk is to present an ongoing work in collaboration with Professor Alessandro Savo, in which we characterize embedded minimal helicoids and totally geodesic hypersurfaces in three-dimensional space-forms through the concept of “constant boundary temperature”, an overdetermined condition involving the Cauchy problem for the heat equation.