## Document Type

Presentation Abstract

## Presentation Date

10-23-2017

## Abstract

Singular integrals comprise a rich area of analysis, the most well known example being the Hilbert Transform. In this talk, we will discuss a singular integral that also intersects geometric measure theory. For functions f:\mathbb{R}^n\rightarrow\mathbb{R} that are C^{1,1} (i.e. the first derivative is Lipschitz continuous), for which 0 is a regular value (i.e. the gradient \nabla f does not vanish on the 0-level set), and whose 0-level set is bounded, there is a not too hard proof that our singular integral computes \mathcal{H}^{n-1}(\{f^{-1}(0)\}), the (n-1)-dimensional Hausdorff measure of the 0-level set of f. We will also briefly mention the simple analysis problem that inspired this research.

**Download the attached PDF to see the abstract with proper math formatting.**

## Recommended Citation

Paxton, Laramie, "Measuring Level Sets of C^{1,1} Functions" (2017). *Colloquia of the Department of Mathematical Sciences*. 531.

https://scholarworks.umt.edu/mathcolloquia/531

## Additional Details

Monday, October 23, 2017 at 3:00 p.m. in Math 103

Refreshments at 4:00 p.m. in Math Lounge 109