Besau, F. G. (2023, September 26). Floating Bodies and Polarity in Non-Euclidean Geometries [Conference Presentation]. Conference on Convex Geometry and Geometric Probability, Salzburg, Austria.
E104-06 - Forschungsbereich Konvexe und Diskrete Geometrie
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Date (published):
26-Sep-2023
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Event name:
Conference on Convex Geometry and Geometric Probability
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Event date:
25-Sep-2023 - 29-Sep-2023
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Event place:
Salzburg, Austria
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Keywords:
Floating Body
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Polarity; Hyperbolic Convex Body; Spherical Convex Body; Affine Surface Area
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Abstract:
Meyer & Werner showed that Lutwak’s p-affine surface area in d-dimensional
Euclidean space arises as the volume derivative of the floating body of convex body con jugated by polarity for p = −d/ (d + 2). We establish an extension of this relation in the
spherical and hyperbolic space. Our results hold in spaces of constant curvature, and we
also show that the Euclidean result of Meyer & Werner can be obtained by a limiting
process as the space curvature tends to zero.
Based on joint work with E. Werner.