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Feb 1 at 7:34 comment added Bernd Ammann Rumors say that experts in geometric measure theory currently have mixed opinions on whether the measure theoretic arguments in this article are complete. For the differential geometers it would be interesting to learn more about this issue, to know whether the problem is settled or whether there are still open cases. Usually such questions are answered by accepting the preprint in a journal as J. Diff. Geom., Annals of Math., Inventiones etc., but it remains unclear why this preprint with great ideas and important consequences has gone another way.
Feb 1 at 7:22 comment added Bernd Ammann What is a bit unusual with this publication is: the article contains definitively great ideas about an important problem, thus it is important to communicate this to the community. However, it was published in a volume in honor of Yau's 70th birthday, although a solution of the positive mass theorem would deserve a much more prestigious journal. Unfortunately, there are no official explanations, and there are young mathematicians who feal unsure whether this result can be safely cited in view of this discrepancy.
Feb 1 at 7:02 comment added Bernd Ammann In the meantime, the article mentioned above was published as follows:Schoen, Richard(1-CA3); Yau, Shing-Tung(1-HRV) Positive scalar curvature and minimal hypersurface singularities.(English summary)Surveys in differential geometry 2019. Differential geometry, Calabi-Yau theory, and general relativity. Part 2, 441–480. Surv. Differ. Geom., 24
Jan 26, 2023 at 19:05 history edited Bernd Ammann CC BY-SA 4.0
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Dec 9, 2019 at 16:54 vote accept Hollis Williams
Dec 9, 2019 at 16:23 history answered Bernd Ammann CC BY-SA 4.0