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Apr 20, 2020 at 13:56 comment added Neal By the way, the first example of an isospectral non-isometric pair is due to Milnor, "Eigenvalues of the Laplace operator on certain manifolds", Proc Natl Acad Sci U S A. 1964 Apr; 51(4): 542 ncbi.nlm.nih.gov/pmc/articles/PMC300113
Jun 25, 2018 at 12:38 comment added Piotr Hajlasz You are right. I did not realize that your argument is self-contained. I was too quick.
Jun 25, 2018 at 6:57 comment added Qiaochu Yuan @Piotr: why? Everything I’ve said is a straightforward exercise. Also I don’t have a reference, because I learned all of this as an exercise that was assigned to me once.
Sep 24, 2015 at 0:44 history answered Qiaochu Yuan CC BY-SA 3.0