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On the uniqueness of certain families of holomorphic disks

Rochon, Frédéric


A Zoll metric is a Riemannian metric whose geodesics are all circles of equal length. Via the twistor correspondence of LeBrun and Mason, a Zoll metric on the sphere S² corresponds to a family of holomorphic disks in CP₂ with boundary in a totally real submanifold P ⊂ CP₂. In this paper, we show that for a fixed P ⊂ CP₂, such a family is unique if it exists, implying that the twistor correspondence of LeBrun and Mason is injective. One of the key ingredients in the proof is the blow-up...[Show more]

CollectionsANU Research Publications
Date published: 2011
Type: Journal article
Source: Transactions of the American Mathematical Society
DOI: 10.1090/S0002-9947-2010-05159-1


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