Local Uniqueness Results for Centroid Bodies

Explore a mathematical lecture on local uniqueness results for centroid bodies. Delve into the examination of convex bodies and hyperplanes satisfying specific conditions such as constant volume cut-off, equal area sections, equal moments of inertia, and equidistance from the origin. Investigate the question posed by Croft, Falconer, and Guy regarding whether any two conditions necessitate the convex body to be a Euclidean ball. Learn about negative results for certain condition pairs and discover positive findings for the combinations (V,I,H) and (V,A,H), as well as cases involving two conditions with additional normalization hypotheses. Gain insights into this collaborative research conducted with D. Ryabogin, A. Stancu, and V. Yaskin, presented by Maria Alfonseca at the Hausdorff Center for Mathematics.