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In April 2017 Schoen and Yau posted on the arxiv their solution of the time-symmetric positive mass theorem in all dimensions, which has been a significant conjecture since the 70s. As of now, July 2020, it hasn't appeared in a journal. Is there any consensus in the geometric analysis community on the veracity of the proof?

https://arxiv.org/abs/1704.05490

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    $\begingroup$ It appears to be a concensus that questions like this one, asking for validity of preprints, are considered off-topic for being too broad. See here: meta.mathoverflow.net/a/942/30186 $\endgroup$
    – Wojowu
    Commented Jul 10, 2020 at 10:36
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    $\begingroup$ It seems like there is a precedent of this rule being broken for notable mathematicians on major conjectures - even in cases where, for what it's worth, the papers are (at least outwardly) "crackpot", which this is not $\endgroup$
    – Quarto Bendir
    Commented Jul 10, 2020 at 15:57
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    $\begingroup$ My (maybe wrong) impression is that Lohkamp's proof is not widely understood, either positively or negatively $\endgroup$
    – Quarto Bendir
    Commented Jul 10, 2020 at 22:31
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    $\begingroup$ It is yet unsatisfactory to see that a major result (over decades) like this is placed in a typically not rigorously peer reviewed collection of invited addresses called "Surveys in Differential Geometry" edited in chief by one of the authors, namely by Yau, and published in a volume on the occasion of his 70's birthday. $\endgroup$
    – GeoViewer
    Commented Jan 6, 2022 at 9:43
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    $\begingroup$ There are certainly some papers citing SY's paper for this result, e.g. by Coley and Ellis, Sakovich and Sormani, and Borghini and Mazzieri. Anyway, Schoen and Yau's approach seems obviously cogent and credible, and and so maybe the best answer to this question would clarify if there are particular parts of their work that are particularly technically demanding (or even possibly unclear). It is disappointing that their paper, along with Lohkamp's, have been out for four years without any (to my knowledge) detailed expository accounts or commentary (whether positive or negative). $\endgroup$
    – Quarto Bendir
    Commented Jan 6, 2022 at 17:54

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