My bachelor's thesis was on the harmonic level set method of Stern and Co and had a lot of fun with it, so this was a great read. I'll have to look at the paper.<p>In general it still feels like there's a lot more to learn about this method (the article mentions the possibility of applications outside the asymptomatically flat case, for more see also section 9 of the survey article [1] of Bray and Co).<p>[1]: <a href="https://arxiv.org/abs/2102.11421" rel="nofollow noreferrer">https://arxiv.org/abs/2102.11421</a>
This was a great read, pretty much as always with Quanta. I'd also never heard of the Huisken-Ilmanen conjecture, and so this sent me down a rabbit hole, which I always enjoy.