Co-area formula for maps into metric spaces

Abstract: 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 a new (and arguably more geometric) proof in that case as well.

classical analysis and ODEsdifferential geometryfunctional analysishistory and overviewmetric geometry

Audience: researchers in the discipline

( paper )

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Online Seminar "Geometric Analysis"

Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

Registration and links to videos available at blatt.sbg.ac.at/onlineseminar.php

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