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Analysis of Contact Cauchy-Riemann maps I: a priori Ck estimates and asymptotic convergence

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Title
Analysis of Contact Cauchy-Riemann maps I: a priori Ck estimates and asymptotic convergence
Author(s)
Yong-Geun Oh; Rui Wang
Publication Date
2018-10
Journal
OSAKA JOURNAL OF MATHEMATICS, v.55, no.4, pp.647 - 679
Publisher
OSAKA JOURNAL OF MATHEMATICS
Abstract
In the present article, we develop tensorial analysis for solutions w of the following nonlinear elliptic system ∂ π w = 0, d(w ∗ λ ◦ j) = 0, associated to a contact triad (M, λ, J). The novel aspect of this approach is that we work directly with this elliptic system on the contact manifold without involving the symplectization process. In particular, when restricted to the case where the one-form w∗λ◦ j is exact, all a priori estimates for w-component can be written in terms of the map w itself without involving the coordinate from the symplectization. We establish a priori Ck coercive pointwise estimates for all k ≥ 2 in terms of the energy density dw2 by means of tensorial calculations on the contact manifold itself. Further, for any solution w under the finite π-energy assumption and the derivative bound, we also establish the asymptotic subsequence convergence to ‘spiraling’ instantons along the ‘rotating’ Reeb orbit.
URI
https://pr.ibs.re.kr/handle/8788114/5424
ISSN
0030-6126
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > Journal Papers (저널논문)
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