Seminars & Colloquia Calendar

Download as iCal file

Complex Analysis and Geometry Seminar

On nonsmooth Frobenius-type theorems and their H\”older estimates

Liding Yao (Ohio State U.)

Location:  Hill Center 705
Date & time: Friday, 24 February 2023 at 10:30AM - 11:30PM


Abstract: 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 a joint work with Brian Street. 

Special Note to All Travelers

Directions: map and driving directions. If you need information on public transportation, you may want to check the New Jersey Transit page.

Unfortunately, cancellations do occur from time to time. Feel free to call our department: 848-445-6969 before embarking on your journey. Thank you.