From: Pascal.Azerad@maths.unine.ch (Pascal A. AZERAD)
Newsgroups: sci.math
Subject: Summary Re: de Rham currents
Date: 11 Nov 92 16:38:29 GMT
Organization: University of Neuchatel, Switzerland

My best thanks to all those who personally answered me.
I thought a summary might be useful to others. In the meantime, I
tried to study De Rham's book,very good indeed though very concise.
For the english-speaking audience it is now published
by Springer under the title "Differentiable manifolds, forms, currents,
harmonic forms" I think.
     We will soon organize an informal seminar here at Neuchatel, 
with someone actually using thoroughly currents in mathematical physics.

Now my question was:
: Bonjour netters!
: I am working in applied mathematics and I would like to use 
: systematically differential forms and de Rham currents. But
: de Rham's famous book is a bit esoteric to me. On the other hand
: most books on differential forms do not mention currents. Currents
: are in a certain sens generalised differential forms, i. e. whose
: coefficients are distributions instead of functions.
: Does anyone know where to find a understandable exposition of the
: theory of currents?
: Thank you.
: -- 
: 	Pascal Azerad                 "Les mathematiques sont simples,
: 	Institut de mathematiques      c'est nous qui sommes compliques."
: 	Universite de Neuchatel
: 	Switzerland.
: 
: 	Pascal.Azerad@maths.unine.ch

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You might try the book "Geometric Measure Theory: A Beginner's Guide" by
Frank Morgan. It's published by Academic Press. The book is intended to be
an introduction to Federer's definitive treatment of Geometric Measure
Theory, but it is a nice introduction to the concepts you mentioned in
your posting.

 -- <<Tim Murdoch>>  (USA)

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You want to look for books on geometric measure theory.  Federer's
book by that title is very good, in a sense, but hard to read.
Fred Almgren's little book on the Plateau problem is a very good
introduction.  I believe there are more recent books, but I can't
give you any references.  Look for books on geometric measure
theory.  The names Allard, Bob Hardt, Almgren might be good clues.

This stuff has been used in geometry a lot, particularly in
the study of minimal surfaces and minimal submanifolds.

This is a little outside of my specialty, which is why I can't
give you any more specific help.

David H. Wagner (USA)

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Essayez 

Morgan, Introduction to Geometric Measure Theory, AcPress
ou
le Chap.3 de Noguchi-Ochiai Geometric Theory of several complex variables, AMS
-- 

Carlos Klimann (France)

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In article <1992Oct28.120638.927@unine.ch> you write:
Connais-tu la "bible" de Dieudonne, Elements d'Analyse? Dans
le chapitre 17 (ou est-ce 18, je ne suis plus sur), il introduit
les courants, mais ce ne sont pas des formes differentielles
avec coefficients dans les distributions, mais plutot des
elements duaux aux formes differentiels. Tout ce que l'on peut
faire avec les formes, on peut le faire avec les formes,
avec la seule difference que l'operateur de bord diminue
le degree. Comme ca, on obtient une theorie de homologie
duale a la theorie de cohomologie de de Rham.

Hope this helps
			Andreas Mueller (Germany)

-- 
	Pascal Azerad                 "Les mathematiques sont simples,
	Institut de mathematiques      c'est nous qui sommes compliques."
	Universite de Neuchatel
	Switzerland.

	Pascal.Azerad@maths.unine.ch
Newsgroups: sci.math