具有 Legendrian 边界条件的接触瞬子:先验估计、渐近收敛和指数公式

IF 0.6 4区 数学 Q3 MATHEMATICS
Yong-Geun Oh, Seungook Yu
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引用次数: 0

摘要

本文通过证明具有 Legendrian 边界条件的接触瞬子的先验椭圆强制估计,建立了具有 Legendrian 边界条件的接触瞬子方程在点状黎曼曲面上的非线性椭圆性,并证明了在均匀 C1 约束下,点状处的渐近指数 C∞ 收敛结果。我们证明了在 Legendrian 边界条件下,接触瞬子在穿刺处的渐近电荷消失。这就消除了沿着里布核出现螺旋尖顶瞬子的现象,从而消除了开弦情况下接触瞬子模量空间紧凑化和弗里德霍尔姆理论的唯一障碍,而这一障碍却困扰着闭弦情况。关于接触瞬子的 C1 估计数和格罗莫夫-弗洛尔-霍费尔式紧凑化细节的研究留给[27]去做,我们还推导出了一个计算模空间虚维度的指数公式。这些结果是后续[27]-[29]和[36]的分析基础,其中包含对接触拓扑学和接触哈密顿动力学的应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Contact instantons with Legendrian boundary condition: A priori estimates, asymptotic convergence and index formula

In this paper, we establish nonlinear ellipticity of the equation of contact instantons with Legendrian boundary condition on punctured Riemann surfaces by proving the a priori elliptic coercive estimates for the contact instantons with Legendrian boundary condition, and prove an asymptotic exponential C-convergence result at a puncture under the uniform C1 bound. We prove that the asymptotic charge of contact instantons at the punctures under the Legendrian boundary condition vanishes. This eliminates the phenomenon of the appearance of spiraling cusp instanton along a Reeb core, which removes the only remaining obstacle towards the compactification and the Fredholm theory of the moduli space of contact instantons in the open string case, which plagues the closed string case. Leaving the study of C1-estimates and details of Gromov-Floer-Hofer style compactification of contact instantons to [27], we also derive an index formula which computes the virtual dimension of the moduli space. These results are the analytic basis for the sequels [27]–[29] and [36] containing applications to contact topology and contact Hamiltonian dynamics.

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来源期刊
CiteScore
1.20
自引率
0.00%
发文量
82
审稿时长
12 months
期刊介绍: The International Journal of Mathematics publishes original papers in mathematics in general, but giving a preference to those in the areas of mathematics represented by the editorial board. The journal has been published monthly except in June and December to bring out new results without delay. Occasionally, expository papers of exceptional value may also be published. The first issue appeared in March 1990.
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