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分析团队系列报告:Quasiconformal geometry and removable sets for conformal mappings

发布人:日期:2021年11月10日 15:02浏览数:

          报告人:Toni Ikonen 博士(University of Jyväskylä)

          时 间:2021年11月9日15:00-16:00

          地 点腾讯线上会议:431 974 494



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 Möbius 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 Jyväskylä) 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
















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