积分平均形式和调和Beltrami微分

数学物理学报 ›› 2025, Vol. 45 ›› Issue (1): 189-202.

积分平均形式和调和Beltrami微分

霍胜进^*(),邵婉婷()

天津工业大学数学科学学院天津 300387

收稿日期:2023-11-23 修回日期:2024-08-10 出版日期:2025-02-26 发布日期:2025-01-08
通讯作者: * 霍胜进, E-mail:huoshengjin@tiangong.edu.cn
作者简介:邵婉婷, E-mail:2810140065@qq.com
基金资助:
国家自然科学基金(12371076);天津自然科学基金(23JCYBJC00730)

Integral Averages forms and Harmonic Beltrami Differentials

Huo Shengjin^*(),Shao Wanting()

Department of Mathematics, Tiangong University, Tianjin 300387

Received:2023-11-23 Revised:2024-08-10 Online:2025-02-26 Published:2025-01-08
Supported by:
NSFC(12371076);TNSFC(23JCYBJC00730)

摘要/Abstract

摘要：

该文主要研究了某些解析函数的积分平均范数和由全纯二次微分所诱导的调和 Beltrami 微分间的关系. 讨论了全纯形式满足哪些条件时具有有限渐近方差. 该文利用积分平均范数给出调和 Beltrami 微分属于 Weil-Petersson 类的判别方法. 进一步给出单位圆周上的拟对称同胚 $g$ 属于 Sobolev $H^{3/2}$ 的判别方法.

关键词: 渐近方差, 调和 Beltrami 微分, Weil-Petersson 类.

Abstract:

In this paper we investigate the relationship between the integral averages norms of some analytic functions and the harmonic Beltrami differentials induced by some holomorphic quadratic differentials. We discuss that under what conditions are the holomorphic forms with finite asymptotic variances. The paper offers a new criterion method for a harmonic Beltrami differential belonging to the Weil-Petersson class by the integral means norms. Furthermore we give a method of determining a homeomorphism $g$ of the unit circle $\partial\Delta$ belonging to Sobolev class $H^{\frac{3}{2}}$ .

Key words: asymptotic variance, harmonic Beltrami differential, Weil-Petersson class.

中图分类号:

O175

霍胜进, 邵婉婷. 积分平均形式和调和Beltrami微分[J]. 数学物理学报, 2025, 45(1): 189-202.

Huo Shengjin, Shao Wanting. Integral Averages forms and Harmonic Beltrami Differentials[J]. Acta mathematica scientia,Series A, 2025, 45(1): 189-202.

参考文献 18

[1]	Astala K, Ivrii O, Perälä A, Prause I. Asymptotic variance of the Beurling transform. Geom Funct Anal, 2015, 25: 1647-1687
[2]	Cui G Z. Integrably asymptotic affine homeomorphisms of the circle and Teichmüller spaces. Sci China Math Ser A, 2000, 43: 267-279
[3]	Eskin A, McMullen C. Mixing counting and equidistribution in Lie group. Duke Math J, 1993, 71(1): 181-209
[4]	Figalli A. On flows of $H^{3/2}$ -vector fields on the circle. Math Ann, 2010, 347: 43-57
[5]	Hedlund G A. Fuchsian groups and Mixtures. Ann of Math, 1939, 40(2): 370-383
[6]	Imayoshi Y, Taniguchi M. An Introduction to Teichmüller Spaces. Tokyo: Springer-Verlag, 1992
[7]	Lehto O. Univalent Functions and Teichmüller Spaces. New York: Springer-Verlag, 1987
[8]	Teo L P. The Velling-Kirillov metric on the universal Teichmüller curve. J Anal Math, 2004, 93: 271-307
[9]	Markovic V. Harmonic diffeomorphisms of nonconpact surfaces and Teichmüller spaces. J London Math Soc, 2002, 65(1): 103-114
[10]	McMullen C T. Thermodynamics, dimension and the Weil-Petersson metric. Invent Math, 2008, 173(2): 365-425
[11]	Nag S. The Complex Analytic Theory of Teichmüller Spaces. New York: Wiley-Interscience, 1988
[12]	Nag S, Verjovsky A. Diff (S¹) and the Teichmüller spaces. Commun Math Phys, 1990, 130(1): 123-138
[13]	Pommerenke C. On the integral means of the derivative of a univalent function. J London Math Soc, 1985, 2(2): 254-258
[14]	Shen Y L. Weil-Peterssen Teichmüller space. Amer J Math, 2018, 140}(4): 1041-1074
[15]	Shen Y L, Tang S A. Weil-Petersson Teichmüller space II: Smoothness of flow curves of $H^{3/2}$ -vector fields. Adv Math, 2020, 359: 106891
[16]	Takhtajan L, Teo L P. Weil-Petersson Metric on the Universal Teichmüller Space. Memo Amer Math Soc, 2006, 183(861): 7-116
[17]	Zhu K H. Bloch type spaces of analytic functions. Rocky Mountain J Math, 1993, 23(3): 1143-1177
[18]	Zhu K H. Operator Theory in Function Spaces. Providence RI: American Math Soc, 2007

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