Mathematics Seminar at ICTP - Thursday 11 July at 16:00 (Guido DE PHILIPPIS)

[ICTP Math Section]

M A T H E M A T I C S   S E M I N A R S  2019


Thursday 11 July, at 16:00 hrs.


Guido De Philippis (SISSA)


Title: Singular two dimensional area minimizing surfaces


Abstract: One of the oldest problem in geometric analysis and in the 
calculus of variations consists  in finding a surface of leat area 
surface spannend by a given smooth curve $\gamma$. The approach of 
Douglas and Rad ensures,  for each prescribed genus, the existence of a 
surface minimizing the area among all the ones with smaller genus. On 
the other hand, after the seminal work of Federer and Fleming, it is 
always possible to find a mass minimizing current spanned by $\gamma$. 
When the Federer fleming solution is smooth (up to the boundary) , it 
naturally coincides with the Dougals Rado solution. In co-dimension one, 
thanks to the seminal work of De Giorgi and Hardt-Simon, this is indeed 
the case. In higher co-dimension the question is not yet completely 
understood and new phenomena might appear. In this talk, after surveying 
the known results,  I will present the construction  of a smooth curve 
in a 4 dimensional Riemannian manifold which spans an area minimizing 
surface with infinite genus. This is based on a joint work with C. De 
Lellis and J. Hirsch.


VENUE:  Luigi Stasi Seminar Room (ICTP Leonardo da Vinci Building, first 
floor)

http://indico.ictp.it/event/8994/

-- 
Koutou Mabilo
ICTP Mathematics Group
Leonardo Da Vinci Building
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