报告题目：Sobolev monotone mappings
报告摘要：An approximation theorem of Youngs (1948) asserts that a continuous map between compact oriented topological2-manifolds (surfaces) is monotone if and only if it is a uniform limit of homeomorphisms. In this talk we discuss analogous approximation results for Sobolev mappings. These results originated in studying variational problems of geometric nature. To build a viable theory we first have to address the question of how to enlarge the class of homeomorphisms to ensure the existence of minimizers. Tadeusz Iwaniec and I introduced Sobolev monotone mappings and established the existence of energy-minimal deformations within the class of such mappings. Related open questions are also discussed.
报告人概况：Jani Oninnen是美国雪城大学和芬兰于韦斯屈莱大学教授，主要研究几个函数论与非线性方程。在具有有限形变映照，Sobolev映照，p-调和方程等研究中取得了一系列重要成果，在JAMS和Invent Math等期刊发表了70多篇高水平论文。