积分平均形式和调和Beltrami微分

积分平均形式和调和Beltrami微分

Integral Averages forms and Harmonic Beltrami Differentials

摘要/Abstract

参考文献 18

相关文章 15

Metrics

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

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)

Shengjin Huo^*(),Wanting Shao()

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：

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.

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

[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

[1]	刘佳, 包雄雄. 非局部时滞扩散方程棱锥形波前解的渐近稳定性[J]. 数学物理学报, 2025, 45(1): 44-53.
[2]	任琛琛, 杨苏丹. 带有渐近概周期系数的次线性热方程解的存在唯一性[J]. 数学物理学报, 2025, 45(1): 31-43.
[3]	潘柔, 陈林. 一类分数阶 $p$ -Kirchhoff 方程多解的存在性[J]. 数学物理学报, 2025, 45(1): 92-100.
[4]	陈雪姣, 李丹丹, 石金诚, 曾鹏. 棱柱体中调和方程对基底扰动的连续依赖性[J]. 数学物理学报, 2025, 45(1): 101-109.
[5]	杨咏丽, 杨赟瑞. 非局部扩散的时空时滞霍乱传染病系统的行波解[J]. 数学物理学报, 2025, 45(1): 110-135.
[6]	李心, 郝文娟, 刘洋. 广义 Brinkman-Forchheimer 方程的渐近性态[J]. 数学物理学报, 2025, 45(1): 74-91.
[7]	吴鹏, 方诚. 具有非局部扩散和空间异质性的年龄-空间结构HIV潜伏感染模型的动力学分析[J]. 数学物理学报, 2025, 45(1): 279-294.
[8]	王晓敏, 吴德玉. 换位子的共轭算子[J]. 数学物理学报, 2024, 44(6): 1426-1432.
[9]	孟志英, 殷朝阳. 具有弱耗散项的 Camassa-Holm 方程的解析性和整体 Gevrey 正则性[J]. 数学物理学报, 2024, 44(6): 1537-1549.
[10]	钱玉婷, 周学良, 程志波. 一类奇性 $\phi$ -Laplacian Rayleigh 型方程周期解的存在性[J]. 数学物理学报, 2024, 44(5): 1183-1193.
[11]	肖苏平, 赵元章. 一类半线性双曲型微分不等式非齐次 Dirichlet 外问题解的存在性与非存在性[J]. 数学物理学报, 2024, 44(5): 1167-1182.
[12]	傅越宸, 倪明康. 一类右端不连续奇异摄动高阶方程组的内部层[J]. 数学物理学报, 2024, 44(5): 1153-1166.
[13]	刘昊麟, 郭合林. 质量临界 Kirchhoff 型方程正规化解的性质[J]. 数学物理学报, 2024, 44(5): 1194-1204.
[14]	孙歆, 段誉. 次线性 Klein-Gordon-Maxwell 系统解的多重性[J]. 数学物理学报, 2024, 44(5): 1205-1215.
[15]	高晓茹, 李建军, 徒君. 一类带有时变系数的分数阶扩散方程解的爆破性[J]. 数学物理学报, 2024, 44(5): 1230-1241.

Just accepted

Online first

Just accepted

Online first

Viewed

Full text

	From	local

	Times	67
	Rate	100%

Abstract

Just accepted	Online first	Issue

0	0	37

From	Others	local

Times	33	4
Rate	89%	11%

Cited

Web of Science	Crossref	ScienceDirect	Search for Citations in Google Scholar >>


This page requires you have already subscribed to WoS.

Shared

Discussed