Timeline for Is the rectifiability of currents independent of the choice of Riemannian metric?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 24, 2020 at 21:13 | comment | added | rozu | Yes indeed, I meant locally rectifiable. | |
| Feb 24, 2020 at 19:48 | history | edited | Weekkola | CC BY-SA 4.0 |
Clarified where I have my definition from
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| Feb 24, 2020 at 19:46 | comment | added | Weekkola | @rozu Thanks for your comment! However, I think you meant locally rectifiable currents, right? After all, I didn't say anything about the boundary. And yes, the mass (and its (un-)boundedness in case the current has non-compact support) can obviously change when the metric changes. Finally, thanks for pointing me at the bi-Lipschitz property – I'll look into that! | |
| Feb 23, 2020 at 15:24 | comment | added | rozu | The way you define it, your class corresponds to the class of "locally integral currents" in Federer's book (see Section 4.1.24 for the definition in Euclidean space). This class is not affected by the change of a metric on a Riemmanian manifold because as metric spaces they are locally bi-Lipschitz equivalent (one can take the identity map). The class of integral currents (assuming they are allowed to have noncompact support) changes in general because a current may have finite mass with respect to one metric but not with respect to another. | |
| S Feb 23, 2020 at 14:50 | history | edited | Weekkola | CC BY-SA 4.0 |
added 101 characters in body
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| Feb 23, 2020 at 14:45 | review | Suggested edits | |||
| S Feb 23, 2020 at 14:50 | |||||
| Feb 18, 2020 at 15:35 | history | edited | Weekkola | CC BY-SA 4.0 |
added 319 characters in body
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| Feb 18, 2020 at 10:10 | history | asked | Weekkola | CC BY-SA 4.0 |