Multidimensional theorems of Teichm\"uller-Wittich-Belinskii type

Mon, 14/05/2012 - 14:00
Speaker: 
Seminar: 
Abstract: 

The classical Teichm\"uller-Wittich-Belinskii theorem implies
the conformality of a planar continuous mapping at a point under rather
general integral restrictions for the dilatation of this mapping
near the point.
This theorem is very rich in applications and has been generalized
by many authors in various directions (weak conformality, differentiability,
multidimensional analogs, etc.).
Certain complete generalizations are due to Reshetnyak and  Bishop, Gutlyanskii, Martio, Vuorinen.

 

I will show in the talk that the assumptions under which the main results have been obtained,

can be essentially weakened and give much stronger estimate
for the limit of $|f(x)|/|x|$ as $x$ approaches $0$.
We essentially improve the underlying modular technique.