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Rigidity of projective area widths and a weighted Crofton formula on $RP^3$
We show that a Riemannian metric on $RP^3$ is a surface Zoll metric if and only if its four projective area widths are equal. We also establish a weighted Crofton formula on $RP^3$ under surface Zoll metrics, from which we derive an inequality relating the systole, the volume, and the common value o
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