The behaviour of Hausdorff dimension under curved 1-dimensional families of projections

Abstract: Given a curve C with nonvanishing geodesic curvature in the unit sphere of R^3, it is an open problem whether the Hausdorff dimension of an arbitrary set A is almost surely preserved under projection onto the orthogonal complements of vectors in C. In this talk I will outline some recent progress on this problem, which makes use of some Fourier restriction tools such as decoupling and wave packet decompositions. Toward the end of the talk I will mention a couple of open problems suggested by the approach.

analysis of PDEsclassical analysis and ODEsfunctional analysis

Audience: researchers in the topic

OARS Online Analysis Research Seminar

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