BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Christian Bär (University of Potsdam) DTSTART:20200714T170000Z DTEND:20200714T180000Z DTSTAMP:20260423T021015Z UID:OSGA/19 DESCRIPTION:Title: Co unter-intuitive approximations\nby Christian Bär (University of Potsd am) as part of Online Seminar "Geometric Analysis"\n\n\nAbstract\nThe Nash -Kuiper embedding theorem is a prototypical example of a counter-intuitive approximation result: any short embedding of a Riemannian manifold into E uclidean space can be approximated by *isometric* ones. As a consequence\, any surface can be isometrically $C^1$-embedded into an arbitrarily small ball in $\\mathbb{R}^3$. For $C^2$-embeddings this is impossible due to c urvature restrictions.\n\nWe will present a general result which will allo w for approximations by functions satisfying strongly overdetermined equat ions on open dense subsets. This will be illustrated by three examples: re al functions\, embeddings of surfaces\, and abstract Riemannian metrics on manifolds.\n\nOur method is based on "weak flexibility"\, a concept intro duced by Gromov in 1986. This is joint work with Bernhard Hanke (Augsburg) .\n LOCATION:https://researchseminars.org/talk/OSGA/19/ END:VEVENT END:VCALENDAR