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I'm trying to read the paper of Jost and Karcher on the existence of harmonic coordinates on a ball whose size only depend on the injectivity radius and a two sided bound on the curvature.

Unfortunately, my german skills are quite low and make the reading really slow. Does there exist another place to find this proof (in English or French) ?

Thanks

flag	asked Dec 7 2010 at 15:11 Thomas Richard 1,452●1●4●11

	You ever tried to ask him personally? mis.mpg.de/de/jjost/index.html He is a very nice person! – Orbicular Dec 7 2010 at 16:39
	Although it's probably too late... I learned a proof from M. Anderson's paper, Convergence and rigidity of manifolds under Ricci curvature bounds, Invent. Math., 1990. (Main Lemma 2.2) – Chih-Wei Chen Sep 26 2011 at 1:33

Willie Wong · Accepted Answer · 2010-12-07 15:23:28Z UTC

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Perhaps Jost's account of it from his lectures on harmonic mapppings between Riemannian manifolds contains a detailed description.

There's also some related results due to Hebey and Herzlich

answered Dec 7 2010 at 15:23

Willie Wong
6,987●20●43

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First, I can confirm that the construction and estimates of almost linear and harmonic co-ordinates appear on the monograph of Jost cited by Willie. I also believe that Anderson and Cheeger prove the existence of harmonic co-ordinates on uniform sized balls using a blow-up argument in their 1992 JDG paper. – Deane Yang Dec 7 2010 at 18:02

Thanks, I found Hebey and Herzlich in the library, it seems nicely written. According to the authors, their proof is the same as the one by Anderson and Cheeger. I'll try to understand these. About Jost monograph, I'll try to have a look on it but it's not in the library of my lab, so it will take longer. Thanks again. – Thomas Richard Dec 7 2010 at 21:55

Harmonic coordinates on Riemannian manifolds

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