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The simplest area-minimizing, codimension one cones $\mathbf{C} \subset \mathbf{R}^{n+1}$ are the Simons cones. I am trying to understand the behavior of area-minimizing cones a bit better, but these cones are 'special' in a variety of ways that most area-minimizing cones are not.

Question. What are the 'next-simplest' cones to consider? The Lawson cones come to mind - is one of them particularly easy to 'see', or particularly instructive in some way? What is your go-to cone when testing some idea?

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    $\begingroup$ Simons cone x R. Not a joke. Considerably different from the Simons cone, eg there is a nonintegrable Jacobi field $\endgroup$
    – Otis Chodosh
    Commented Oct 30, 2022 at 3:04
  • $\begingroup$ Can you define Simons cones? $\endgroup$
    – Anton Petrunin
    Commented Oct 30, 2022 at 17:22
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    $\begingroup$ @OtisChodosh Thanks Otis, I'll keep that in mind - I didn't expect this answer! PS. I hope it's OK if I leave the question open for now; I'm curious what comments other people might have. $\endgroup$
    – Leo Moos
    Commented Nov 4, 2022 at 13:08

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