Timeline for Generalization of area and coarea formula for fractional Hausdorff measures
Current License: CC BY-SA 4.0
7 events
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| May 31, 2021 at 11:45 | history | edited | YCor | CC BY-SA 4.0 |
edited tags, fixed capitals
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| May 31, 2021 at 9:43 | history | edited | Johannes Hahn | CC BY-SA 4.0 |
Fixed typo
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| Mar 5, 2020 at 4:41 | answer | added | Behnam Esmayli | timeline score: 5 | |
| Feb 12, 2020 at 4:08 | comment | added | Behnam Esmayli | e-collection.library.ethz.ch/eserv/eth:289/eth-289-02.pdf Here a co-area formula is proven for maps from Euclidean $\mathbb{R}^{n+m} \to (X,d)$ where $X$ is an $\mathcal{H}^n$-$\sigma$-finite metric space. The Jacobian there is defined via the "metric derivative" of $f$. The metric differential exists at a.e point of domain and is a seminorm on $\mathbb{R}^{n+m}$. If the kernel of the seminorm is nontrivial then Jacobian is zero, and when it is a norm its Jacobain is ratio of the volume of its unit ball to that of the usual Euclidean ball. Hope this helps! And why interested in this?! | |
| Dec 22, 2016 at 8:52 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
deleted 1 character in body
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| Dec 22, 2016 at 8:03 | comment | added | Longyearbyen | A very general Coarea formula for integer Hausdorff measure is proved in Federer's book, 3.2.22. Never heard for fractional ones. | |
| Dec 21, 2016 at 23:04 | history | asked | Johannes Hahn | CC BY-SA 3.0 |