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Abstract: A Zoll metric is a Riemannian metric whose geodesics are all circles of equallength. Via the twistor correspondence of LeBrun and Mason, a Zoll metric onthe 2 dimensional sphere corresponds to a family of holomorphic disks in CP 2with boundary in a totally real submanifold P. In this paper, we show that fora fixed totally real submanifold P, such a family is unique if it exists,implying that the twistor correspondence of LeBrun and Mason is injective. Oneof the key ingredients in the proof is the blow-up and blow-down constructionsin the sense of Melrose.



Author: Frederic Rochon

Source: https://arxiv.org/



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