slideshow 3

Seminar on theory of function spaces

Co-area formula for maps into metric spaces

Benham Esmayli
University of Pittsburgh

 

Thursday, 10. December 2020 - 15:40 to 17:40

On-line seminar; for the access data write to Luboš Pick pick@karlin.mff.cuni.cz.

Co-area formula for maps between Euclidean spaces contains, as its very special cases, both Fubini's theorem and integration in polar coordinates formula. In 2009, L. Reichel proved the coarea formula for maps from Euclidean spaces to general metric spaces. I will discuss a new proof of the latter by the way of an implicit function theorem for such maps. An important tool is an improved version of the coarea inequality (a.k.a Eilenberg inequality) that was the subject of a recent joint work with Piotr Hajlasz. Our proof of the coarea formula does not use the Euclidean version of it and can thus be viewed as new (and arguably more geometric) in that case as well.