Researches of fundamental and applied properties for Modern Loewner Theory

2016 Fiscal Year Final Research Report

• Project/Area Number: 26800053
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Yamaguchi University (2015-2016); Tokyo Institute of Technology (2014)
• Principal Investigator: Hotta Ikkei 山口大学, 創成科学研究科, 講師 (10725237)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: レブナー方程式 / 着等角写像 / 等角写像 / シュラム・レブナー発展

Outline of Final Research Achievements

Recently a new approach to treat evolution families and Loewner chains in a quite general framework has been suggested. It enables us to describe a variety of the dynamics of one-parameter family of conformal mappings. In this research project, we have investigated fundamental and properties and applications of Modern Loewner Theory, including relations between evolution families and Herglotz functions, and sufficient conditions of quasiconformal extensions for chordal/Ld-Loewner chains. These results were published in international mathematical journals, and presented in many international/domestic conferences.

Free Research Field

解析学基礎