@InProceedings{patakova_et_al:LIPIcs.SoCG.2020.62, author = {Pat\'{a}kov\'{a}, Zuzana and Tancer, Martin and Wagner, Uli}, title = {{Barycentric Cuts Through a Convex Body}}, booktitle = {36th International Symposium on Computational Geometry (SoCG 2020)}, pages = {62:1--62:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-143-6}, ISSN = {1868-8969}, year = {2020}, volume = {164}, editor = {Cabello, Sergio and Chen, Danny Z.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.62}, URN = {urn:nbn:de:0030-drops-122201}, doi = {10.4230/LIPIcs.SoCG.2020.62}, annote = {Keywords: convex body, barycenter, Tukey depth, smooth manifold, critical points} }