BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sven Pistre (RWTH Aachen University) DTSTART:20200609T170000Z DTEND:20200609T180000Z DTSTAMP:20260423T035030Z UID:OSGA/18 DESCRIPTION:Title: Th e Radon transform and higher regularity of surfaces minimising a Finsler a rea\nby Sven Pistre (RWTH Aachen University) as part of Online Seminar "Geometric Analysis"\n\n\nAbstract\nA Finsler metric is a smooth family o f smooth norms on the tangent bundle of a manifold. One possible generalis ation of the usual Riemannian notion of area in Finsler geometry is the Bu semann-Hausdorff area functional. In this talk I will consider high-codime nsional disk-type surfaces which minimise this area with respect to Platea u boundary conditions. $\\\\$\nI will show that the Busemann-Hausdorff are a functional fits into the Hildebrandt-von der Mosel framework on Cartan f unctionals. Existence of minimisers is then guaranteed under mild growth c onditions of the Finsler metric. Higher regularity ($W^{2\,2}_{\\textrm{lo c}} \\cap C^{1\,\\mu}$) of minimisers can be achieved by using functional analytic properties of the Radon transform. \n$\\\\$\nThe latter is an ope rator which assigns a function on the $(n−1)$-sphere its mean by integra tion over $(m-1)$-dimensional subspheres. One crucial property of this ope rator is its equivariance with respect to a Lie group action on the sphere and the $m$-Grassmannian. An infinitesimal version of this equivariance y ields the regularity results about area minimisers.\n LOCATION:https://researchseminars.org/talk/OSGA/18/ END:VEVENT END:VCALENDAR