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This is a two-volume collection presenting the selected works of Herbert Busemann, one of the leading geometers of the twentieth century and one of the main founders of metric geometry, convexity theory and convexity in metric spaces. Busemann also did substantial work (probably the most important) on Hilbert’s Problem IV. These collected works include Busemann’s most important published articles on these topics.   Volume I of the collection features Busemann’s papers on the foundations of geodesic spaces and on the metric geometry of Finsler spaces.    Volume II includes Busemann’s papers on convexity and integral geometry, on Hilbert’s Problem IV, and other papers on miscellaneous subjects.  Each volume offers biographical documents and introductory essays on Busemann’s work, documents from his correspondence and introductory essays written by leading specialists on Busemann’s work. They are a valuable resource for researchers in synthetic and metric geometry, convexity theory and the foundations of geometry. 

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9783319656236

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Herbert Busemann (1905-1994) was one of the most original geometers of the twentieth century, and one of the main founders of metric methods in geometry. His work brought together the axiomatic geometry of Hilbert, Minkowski's work on convex bodies, and the differential geometry that had blossomed in the 1920s and 1930s – but that only caught up with his insistence on global results after the “im grossem” revolution of the 1960s. A geometer well ahead of his time, Busemann pioneered topics such as the theory of calibrations, global differential geometry and the geometry of normed spaces. His works are a gold mine of ideas and problems that will continue to influence research in convex and metric geometry. Busemann's originality is accompanied by a return to the sources, that is, to the most fundamental elements of geometry. The techniques he introduced and the problems he formulated have a considerable influence on modern research and seem poised to continue that influence well into the future.

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