Analysis of Matching Mass Distributions

匹配质量分布分析

• 批准号: RGPIN-2014-05448
• 负责人: Kim, YoungHeon
• 金额: $ 1.68万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635326
• 关键词: Analysis; Matching; Mass; Distributions

The proposed research concerns optimal transport theory which addresses problems arising when two or more mass distributions are to be matched in a most efficient way, minimizing a transportation cost of moving mass from one location to another. A focus will be on developing mathematical methods for understanding the nature of singularities of optimal transport maps, which may occur due to lack of sufficient geometrical conditions on the cost and the mass distributions. This will be considered for transportation on curved landscapes. Also, a substantial effort will be devoted to the case of many mass distributions to be matched. Another goal is to develop a theory for an optimal transport problem which models the situation where a mass distribution is transported along channels with limited capacities. This research will have significant impact on the optimal transport theory, by giving important results on the fundamental properties of optimal transport phenomena, which have many current and potential applications in mathematical analysis and geometry, mathematical economics, probability theory, fluid/continuum mechanics, meteorology, and biology, among others.

所提出的研究涉及最佳运输理论，该理论解决了当两个或多个质量分布以最有效的方式匹配时出现的问题，最大限度地减少将质量从一个位置移动到另一个位置的运输成本。重点将是开发数学方法来理解最佳传输图奇点的性质，这可能是由于成本和质量分布缺乏足够的几何条件而发生的。这将被考虑用于弯曲景观上的运输。此外，将投入大量精力来处理许多要匹配的质量分布的情况。另一个目标是开发一种最优运输问题的理论，该理论模拟沿着容量有限的渠道运输大量分布的情况。这项研究将对最佳输运理论产生重大影响，通过对最佳输运现象的基本性质提供重要结果，在数学分析和几何、数理经济学、概率论、流体/连续力学、气象学等方面有许多当前和潜在的应用和生物学等。