User talk:Camillo.delellis

Hi Camillo, I have tried to add some MR/ZBL data to your pages. Please check. There are certainly erroneous choices, but I hope some will help. Sorry it took me so long to do this, however, I was pretty much occupied by various other things and only had very little time for EoM recently, to my serious regret! I appreciate your work very much! --Ulf Rehmann 15:14, 27 September 2012 (CEST)

Hi Ulf, I just checked a couple and even though I will have to manually add/correct some entries, it surely saves a lot of time! I will slowly check them all: when I proceed updating/texing the pages (or proofreading the ones I have already rewritten) I will also take care of the MR/ZBL. Thanks a lot. Camillo (talk) 09:12, 28 September 2012 (CEST)

Camillo, if you want to use "nowiki", do like that (look at the source text!) $E=mc^2$ (note only one "/"). But this is not the way to correct formulas... --Boris Tsirelson (talk) 13:47, 16 August 2013 (CEST)

It was an early attempt at correcting the formulas, after reading the first post of Ulf. I then read the other posts and made the "right" corrections... but I forgot about a coule of nowiki's. Thanks for removing them. I think there are no more of them around. Camillo (talk)

Math question

Camillo, may I ask you a math question? It seems, you are just the expert needed. I know that a differential k-form on R^n may be integrated over a singular cube, the latter being a smooth map of the k-cube to R^n. What happens if the map is Lipschitz (rather than smooth)? I guess the integration is still possible, that is, we get a current. I even guess that this is written in Whitney 1935 "r-dimensional integration in n-space". But I am far from being sure. (Is my question very naive for experts?) Thank you beforehand, Boris Tsirelson (talk) 17:07, 5 February 2014 (CET)

Absolutely. You can define the integration pulling back the form on the $k$-cube: since the Lipschitz map is differentiable almost everywhere (with bounded partial derivatives), the pull back will be of the form $f dx_1\wedge \ldots \wedge dx_k$, with $f$ Borel measurable and $L^1$. So your integral will simply be the Lebesgue integral $\int f$. This defines a current which belongs to the, perhaps, best studied (and in a sense also best behaving) class of currents, which are called integral currents. The question is not naive, but just touching the basics of geometric measure theory (more specifically the basics of Federer-Fleming theory). It might indeed be Whitney the first to consider such objects, but they became quite popular in analysis and geometry only after the 1960 paper of Federer and Fleming. Camillo (talk) 07:05, 6 February 2014 (CET)