Comments on: Sectors with Density in Granada
https://sites.williams.edu/Morgan/2009/07/18/sectors-with-density-in-granada/
Math, Teaching, and Other Items of InterestTue, 21 Oct 2014 09:46:48 +0000
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By: Frank Morgan » Blog Archive » Manifolds with Density: Fuller References
https://sites.williams.edu/Morgan/2009/07/18/sectors-with-density-in-granada/#comment-14049
Tue, 21 Oct 2014 09:46:48 +0000http://blogs.williams.edu/Morgan/?p=31#comment-14049[…] [2012] Alexander Díaz, Nate Harman, Sean Howe, David Thompson, Isoperimetric problems in sectors with density, Adv. Geom. 12 (2012), 589–619; arXiv.org (2010); see blog posts 1 and 2. […]
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By: Sean Howe
https://sites.williams.edu/Morgan/2009/07/18/sectors-with-density-in-granada/#comment-85
Sun, 19 Jul 2009 16:15:46 +0000http://blogs.williams.edu/Morgan/?p=31#comment-85Right now we know that for density the circular arc minimizes up until the π/(p+1) sector. We could improve that to the π/(p/2+1) sector if we could show that in the plane with regular area and perimeter density for circles about the origin were minimizers. Indeed, the entire conjecture has an equivalent statement in terms of the plane with different area and perimeter densities, but this is a particularly nice case. Furthermore the line p/2+1 is the tangent line at p=0 to √(p+1) so this is the best possible linear (in the denominator) estimate we could get.
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