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Exponential decay estimates and smoothness of the moduli space of pseudoholomorphic curves

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arxiv 1603.07026 v2 pith:TPZQI5OC submitted 2016-03-22 math.SG math.DG

Exponential decay estimates and smoothness of the moduli space of pseudoholomorphic curves

classification math.SG math.DG
keywords decayexponentialcurvespseudoholomorphicsmoothnesschangegivenlength
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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In this paper, we examine the dependence of standard gluing process for pseudoholomorphic curves under the change of the length $T$ of the neck-region with respect to the cylindrical metrics associated to the given analytic coordinates near the punctures in the setting of bordered open Riemann surface with boundary punctures. We establish exponential decay of the $T$-derivatives of the $T$-dependent family of glued solutions under the change of the length $T$ of the neck-region in a precise manner. This exponential decay estimate is an important ingredient to prove the smoothness of the Kuranishi structure constructed on the compactified moduli space of pseudoholomorphic curves given in the appendix of the authors' book. We also demonstrate the way how this smoothness follows from the exponential decay.

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Cited by 3 Pith papers

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