On the uniqueness of certain families of holomorphic disks

Details On the uniqueness of certain families of holomorphic disks On the uniqueness of certain families of holomorphic disks

2007-09-07

arxiv.org/abs/0709.1118v2

Mathematics

Differential Geometry

24 pages, 8 figures, improved the notation, removed the last section, corrected typos

Scientific paper

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 2 dimensional sphere corresponds to a family of holomorphic disks in CP_2 with boundary in a totally real submanifold P. In this paper, we show that for a fixed totally real submanifold P, 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 and blow-down constructions in the sense of Melrose.

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