Nandakumar R
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On comparing planar convex regions of equal perimeter and area
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We suggest an answer to question 1 above, without proof of optimality: First we note two facts. Please see https://nandacumar.blogspot.com/2012/11/maximizing-and-minimizing-diameter-ii.html for some ...

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On 'fair bisectors' of planar convex regions
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An answer to the question 2 (written with K Sheshadri) The guess made above that needs to be proved: For a general convex polygonal region with no symmetries, for every orientation, we have a unique ...

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