Talk:Positive energy theorem

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Still open?[edit]

According to a paper by H. L. Bray from 2001: "The Positive Mass Theorem is also technically still open in dimensions 8 and higher for manifolds which are not spin."

Has some progress been made?

201.21.57.71 (talk) 00:57, 5 August 2015 (UTC)[reply]

@Gumshoe2: Do you know? Dennui (talk) 18:01, 4 July 2020 (UTC)[reply]

I am not quite an expert in this. Schoen and Yau's 2017 article https://arxiv.org/abs/1704.05490 has not yet appeared in a journal, but has been cited quite a bit by other authors. It claims to definitively resolve the conjecture in the "time-symmetric and asymptotically flat case". It seems like Schoen and Yau's Jang equation approach in their 1981 paper should extend to give the general "asymptotically flat" case, but this would require some new technical innovations parallel to the innovations in their 2017 article. As far as I know, this hasn't been resolved.

I really need to clean up this article at some point to make it more readable, without all these separate "versions". If anyone else wants to do it, an optimal version should probably make use of Christodoulou and O'Murchadha's boost theorem and of Lohkamp's reduction to the compact case. Gumshoe2 (talk) 18:52, 4 July 2020 (UTC)[reply]

Thank you very much for your answer! Really appreciated it. ^^ Dennui (talk) 19:08, 4 July 2020 (UTC)[reply]