Title：On Sobolev maps between manifolds and branched transportation
Speaker：Fabcrice Béthuel(Sorbonne Université)
Time：Friday, October27,15:00-16:00
Location：Mingde Building, B201-1
Abstract：In the talk, I wish to stress the link between branched transportationtheory, and some issues in the study of Sobolev maps between manifold. Inparticular, I will present a counterexample to the sequential weak density ofsmooth maps between two manifoldsandin the Sobolev space1,(, ), in the caseis an integer. It has been shown quite a while agothat, if< = ()is not an integer and the[]-th homotopy group[]()ofis not trivial,[]denoting the largest integer less than, thensmooth maps are not sequentially weakly dense in1,(, ). On the otherhand, in the case<is an integer, examples of specific manifoldsandhave been provided where smooth maps are sequentially weakly dense in1,(, )with[]() ≠ 0, although they are not dense for thestrongconvergence. This is the case for instance for=. Such a property doesnot hold for arbitrary manifoldsand integers.
About the speaker：
Fabrice Béthuel现任法国索邦大学教授，数学硕士研究生负责人。Fabrice Béthuel是世界著名数值分析和偏微分方程专家，法国大学研究院院士，世界数学家大会特邀报告人，获得过众多国际大奖，比如法国科学院Mergier-Bourdeix Prize，FERMAT Prize和IBM Prize，担任或曾担任国际重要数学杂志编委，比如欧洲数学会杂志(Journal of European Mathematical Societty)和泛函分析杂志(Journal of Functional Analysis).
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