On nonsmooth Frobenius-type theorems and their Hölder estimates
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：姚力丁（美国俄亥俄州立大学）
：2023-06-21 10:00
：海韵园数理大楼天元会议室686报告厅
报告人：姚力丁（美国俄亥俄州立大学）
时 间：2023年6月21日上午10:00
地 点：海韵园数理大楼686会议室
内容摘要:
In this talk I will discuss several results from my thesis concerning the integrable structures on manifolds. The Frobenius-type theorems describe the necessary and sufficient conditions on a locally integrable structure for when it is equal to the span of (some real and complex) coordinate vector fields. The typical examples are:
- The Frobenius theorem, that an involutive real subbundle is spanned by some real coordinate vector fields.
- The Newlander-Nirenberg theorem, that an involutive almost complex structure is spanned by some complex coordinate vector fields.
- Nirenberg’s complex Frobenius theorem, which is the combination of the above two cases.
In the talk we will introduce the involutive condition with weakest regularity assumption. We obtain the Frobenius theorem when the subbundle is only log-Lipschitz continuous. For a $C^{k,s}$ complex Frobenius structure, we show that there is a $C^{k,s}$ coordinate chart such that the structure is spanned by coordinate vector fields that are $C^{k,s−\epsilon}$ for all $\epsilon >0$, where the $\epsilon>0$ loss in the result is optimal. This is partly joint with Brian Street.
个人简介：
姚力丁，俄亥俄州立大学博士后研究员，2022年博士毕业于威斯康星大学麦迪逊分校。研究方向是调和分析、多复变函数、函数空间及其应用，相关研究成果发表于J. Funct. Anal., J. Fourier Anal. Appl., J. Geom. Anal., J. Anal. Math., Proc. Amer. Math. Soc.等学术期刊上。
联系人：杨东勇
