The Parabolic Density Problem – Andrea Merlo (Universidad del Pais Vasco)


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In this talk, I will present the solution to the density problem in parabolic spaces in codimension 1 for the Koranyi norm. In addition to discussing classical connected topics such as quantitative structural properties of uniform measures, we will provide a counterexample to the immersed version of Preiss’s rectifiability criterion in the parabolic plane for the box norm. Further, we will also show how certain square functions of the density imply the bilateral weak geometric lemma.

Finally, we will prove that such square function estimates do not imply uniform parabolic rectifiability in a very strong sense. The measure exhibiting this behavior will be constructed using elementary Fourier techniques.

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