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Jun 15, 2016 at 16:29 comment added Neal By smoothing the rectangles in this example, one can also produce smooth convex domains which do not have monotonicity, and relaxing convexity, there are also counterexamples among annuli. See Ni-Wang, "On the First Positive Neumann Eigenvalue."
Jun 15, 2016 at 16:19 vote accept Sharpie
Jun 15, 2016 at 11:07 vote accept Sharpie
Jun 15, 2016 at 13:46
Jun 15, 2016 at 3:35 history edited Christian Remling CC BY-SA 3.0
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Jun 15, 2016 at 3:23 history answered Christian Remling CC BY-SA 3.0