[{"key":"dc.contributor.author","value":"Langharst, Dylan","language":null},{"key":"dc.date.accessioned","value":"2026-05-04T05:00:52Z","language":null},{"key":"dc.date.available","value":"2026-05-04T08:39:35Z","language":null},{"key":"dc.date.issued","value":"2026-04-30","language":null},{"key":"dc.identifier.other","value":"BIRS-VIDEO-202604301045-Langharst","language":null},{"key":"dc.identifier.other","value":"BIRS-VIDEO-26w5574-59060","language":null},{"key":"dc.identifier.uri","value":"http:\/\/hdl.handle.net\/2429\/94301","language":null},{"key":"dc.description.abstract","value":"In 1998, Richard Gardner and Gaoyong Zhang introduced the radial pth mean bodies $R_pK$ of a convex body K for $p>-1$. Furthermore, they established that $R_pK$ are convex when $p\\ge 0$, but the convexity in the regime $(-1,0)$ remained unresolved. In this talk, we answer this nearly 30-year-old question in the affirmative. Along the way, we provide a new proof of Keith Ball's theorem on integrals of log-concave functions along rays against the weight $r^{p-1}$ and introduce an extension to negative $p$.","language":null},{"key":"dc.format.extent","value":"34.0 minutes","language":null},{"key":"dc.format.mimetype","value":"video\/mp4","language":null},{"key":"dc.language.iso","value":"eng","language":null},{"key":"dc.publisher","value":"Banff International Research Station for Mathematical Innovation and Discovery","language":null},{"key":"dc.relation","value":"26w5574: Applications of Harmonic Analysis to Convex Geometry","language":null},{"key":"dc.relation.ispartofseries","value":"BIRS Workshop Lecture Videos (Banff, Alta)","language":null},{"key":"dc.rights","value":"Attribution-NonCommercial-NoDerivatives 4.0 International","language":null},{"key":"dc.rights.uri","value":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/","language":null},{"key":"dc.subject","value":"Mathematics","language":null},{"key":"dc.subject","value":"Functional\/complex Analysis","language":null},{"key":"dc.subject","value":"Harmonic Analysis On Euclidean Spaces","language":null},{"key":"dc.subject","value":"Convex And Discrete Geometry","language":null},{"key":"dc.title","value":"Radial Mean Bodies Are Convex","language":null},{"key":"dc.type","value":"Moving Image","language":null},{"key":"dc.description.affiliation","value":"Non UBC","language":null},{"key":"dc.description.reviewstatus","value":"Unreviewed","language":null},{"key":"dc.description.notes","value":"Author affiliation: Carnegie Mellon University","language":null},{"key":"dc.description.scholarlevel","value":"Postdoctoral","language":null},{"key":"dc.date.updated","value":"2026-05-04T05:00:53Z","language":null}]