"Non UBC"@en . "DSpace"@en . "Dann, Susanna"@en . "2017-12-04T06:01:35Z"@* . "2017-05-25T15:09"@en . "A flag area measure on a finite-dimensional euclidean vector\nspace is a continuous translation invariant valuation with values in the\nspace of signed measures on the flag manifold consisting of a unit vector\n$v$ and a $(p + 1)$-dimensional linear subspace containing $v$.\n\nUsing local parallel sets, Hinderer constructed examples of $SO(n)$-\ncovariant flag area measures. There is an explicit formula for his \nflag area measures evaluated on polytopes, which involves the squared cosine\nof the angle between two subspaces.\n\nWe construct a more general space of $SO(n)$-covariant \nflag area measures, which satisfy a similar formula for polytopes, but with an arbitrary elementary symmetric polynomial in the squared cosines of the\nprincipal angles between two subspaces. Hinderer's \nflag area measure\ncorrespond to the special case where the elementary symmetric polynomial is just the product.\n\nWe also provide a classification result in the spirit of Hadwiger's\ntheorem. We introduce a natural notion of smoothness and show that\nevery smooth $SO(n)$-covariant flag area measure is a linear combination\nof the ones which we constructed.\n\nJoint work with Judit Abardia-Ev\'equoz and Andreas Bernig."@en . "https://circle.library.ubc.ca/rest/handle/2429/63801?expand=metadata"@en . "32 minutes"@en . "video/mp4"@en . ""@en . "Author affiliation: Vienna Institute of Technology"@en . "10.14288/1.0361152"@en . "eng"@en . "Unreviewed"@en . "Vancouver : University of British Columbia Library"@en . "Banff International Research Station for Mathematical Innovation and Discovery"@en . "Attribution-NonCommercial-NoDerivatives 4.0 International"@en . "http://creativecommons.org/licenses/by-nc-nd/4.0/"@en . "Postdoctoral"@en . "BIRS Workshop Lecture Videos (Banff, Alta)"@en . "Mathematics"@en . "Convex and discrete geometry"@en . "Geometry"@en . "Discrete mathematics"@en . "Flag area measures"@en . "Moving Image"@en . "http://hdl.handle.net/2429/63801"@en .