Thursday, 19 December 2019, 2.30 p.m. (sharp),

Dr. Jonas Hirsch, University of Leipzig

at the conference room of Dipartimento di Matematica "F. Casorati" - aula C29(Lavandino),in Pavia, will give a lecture titled:

NONCLASSICAL MINIMIZING SURFACES WITH SMOOTH BOUNDARY

At the end a refreshment will be organized.

---------------------------------------------------------

Abstract. We construct a Riemannian metric g on R^4 (arbitrarily close
to the euclidean one) and a smooth simple closed curve Γ ⊂ R^4 such
that the unique area minimizing surface spanned by Γ has infinite
topology. Furthermore the metric is almost Kaehler and the area
minimizing surface is calibrated. This example suggests that a
conjecture by B. White is sharp. It states that the Federer-Fleming
solution has finite topology if the boundary curve Γ ⊂ R^n is real
analytic. If White's conjecture were true, then for real analytic
boundary curves the Federer-Fleming solution T would coincide with the
Douglas-Rado solution for some genus g. In co-dimension one this holds
true already if the boundary curve Γ is sufficiently regular (C^{k,α}
for k + α > 2) as a consequence of De Giorgi's interior regularity
theorem and Hardt-Simon’s boundary regularity result. In contrast by
our example the situation seems to change dramatically if we go to
higher co-dimension. In my talk I would like to present the
construction of our example and its link to the known boundary
regularity result in higher co-dimension.
Joint work with C. De Lellis and G. De Philippis.