报告题目：Quasiconformal geometry and removable sets for conformal mappings

报 告 人：Toni Ikonen（University of Jyvaskyla，芬兰）

报告时间：2021年11月9日  15:00-16:00

报告地点：腾讯会议（431974494）

报告摘要：

We are interested in constructing metric spaces by studying lower semicontinuous weights in the plane. Given such a weight, one can define a length distance as in the classical Riemannian setting and study the regularity of the space. We are interested in locally bounded weights that vanish on a Cantor set in the plane, in which case the construction always defines a length distance. We want to understand when the constructed length space admits a quasiconformal parametrization by a Riemannian surface. We provide a sufficient condition on the " allowed" Cantor sets: A compact set is removable for conformal mappings if conformal maps defined on its complement are restrictions of Mobius transformations. Such sets are always Cantor sets and every weight vanishing on it yields a length space admitting a quasiconformal parametrization by a Riemannian surface. We also discuss a suitable converse of this result.

The talk is based on the joint work "Quasiconformal geometry and removable sets for conformal mappings" (to appear in J. Anal. Math.) with Matthew Romney.

报告人简介：

Toni Ikonen，男，于韦斯屈莱大学（University of Jyvaskyla）博士，导师是Kai Rajala教授。研究领域为单复变，更具体的研究内容是二维度量曲面上的拟共形单值化（quasiconformal uniformization）问题。在J. Anal. Math, Ann. Acad. Sci. Fenn. Math, Proc. Amer. Math. Soc., Anal. Geom. Metr. Spaces等国际知名SCI刊物接收和发表多篇论文。