Mathematical Sciences: Problems in Potential Theory

数学科学：势论问题

• 批准号: 9400687
• 负责人: Jang-Mei Wu
• 金额: $ 6万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-15 至 1997-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9400687&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Potential; Theory

9400687 Wu This award supports mathematical research on problems arising from the classical theory of complex analysis and potential theory approached from several new points of view. The work concerns investigations into the nature of null sets for doubling measures and related problems on quasiconformal mapping. In particular the question of whether null sets of quasisymmetric homeomophisms on the unit circle are invariant under bilipschitz homeomorphisms. Work will also continue on harmonic measures for uniformly elliptic partial differential operators. Particular emphasis will be placed on building operators on the positive orthant by genuinely n-dimensional methods so that the support of the corresponding harmonic measures have small Hausdorff dimensions. Effort will be made to investigate practical ways of estimating expected lifetime for conditional Brownian motion for domains satisfying a capacity density condition. A new characterization of such domains is expected to result. Research in complex analysis and potential theory focuses on problems related to real and complex functions of several variables which satisfy certain partial differential equations. The theory is highly geometric and methods for attacking the many important problems are drawn from a multitude of mathematical theories such as probability, differential geometry, differential equations and functional analysis. ***

小行星9400687 该奖项支持数学研究所产生的问题，从古典理论的复杂分析和潜在的理论，从几个新的角度来探讨。 研究了加倍测度的空集的性质及拟共形映射的相关问题。 特别是单位圆上的拟对称同胚的空集在bilipschitz同胚下是否不变的问题。 工作也将继续调和措施的一致椭圆偏微分算子。 特别强调将放在建设运营商的正正交真正的n维方法，使支持相应的调和措施有小Hausdorff尺寸。 努力将调查的实际方法估计预期寿命的条件布朗运动的域满足容量密度条件。 一个新的表征，这样的领域预计结果。复分析和位势理论的研究主要集中在与满足某些偏微分方程的多元真实的和复变函数有关的问题上。该理论是高度几何和方法攻击的许多重要问题是来自众多的数学理论，如概率，微分几何，微分方程和功能分析。 ***