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I am trying to get some insights for the combinatorial argument of Pitts (in his PhD thesis 'Existence and regularity of minimal surfaces in Riemannian manifolds', Princeton University Press, 1981) to prove the existence of suitable class of varifolds in the so-called Almgren-Pitts theory. Pitts quotes the reference 'The theory of varifolds' (Almgren, mimeographed notes, Princeton, 1965) as the origin of his argument.

Unfortunately, I have no idea where to find this text, so any help would be very appreciated.

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3 Answers 3

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Here is the story behind these notes, and a redirect to On the First Variation of a Varifold, W.K. Allard (1972).

a quote from: Selected Works of Frederick J. Almgren

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  • $\begingroup$ Thank you very much for your answer Prof. Beenakker. I know the reference of Allard, but I think there is nothing relating to the combinatorial argument. So I will not close the question immediately. $\endgroup$
    – Paul-Benjamin
    Commented Feb 4, 2016 at 8:22
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I just bumped into your post after doing some google search to find a bibtex entry for Almgren's notes.

I have a copy of them: I could copy it and send it to you (or maybe scan it and share it via dropbox). However before getting to the combinatorial arguments you would have to go through quite a lot of material. I am writing a paper with a PhD student where we modify Pitts' theory for the case of surfaces with boundaries and we have a separate section with the relevant combinatorial argument, which is probably easier to understand. If you are interested please contact me by email. My name is Camillo De Lellis and I work at the math department of the University of Zuerich: you find my email address in my web page there

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  • $\begingroup$ Dear Prof. De Lellis, thank you very much for your extremely generous offer, but I managed to get a printed copy in the meantime. $\endgroup$
    – Paul-Benjamin
    Commented Aug 17, 2016 at 13:32
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This question has already an accepted answer and it was long inactive: nevertheless I find compelling to say what I just found by googling the internet. It seems that recently the IAS has started a Digital Repository. It is called Albert, and between the other notes available as -pdf scans, they made available Almgren's ones: a direct link is given below in the "Reference" section, so every researcher seeking an answer to the above or any other related question will benefit from them.

Reference

[1] Frederick J. Almgren, “The Theory of Varifolds : A Variational Calculus in the Large for the $k$-Dimensional Area Integrand.” Institute for Advanced Study, -1, 1964.

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