Integral geometry of pairs of hyperplanes or lines
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DOI: 10.1007/s00013-020-01465-0
Abstract: Crofton’s formula of integral geometry evaluates the total motion invariant measure of the set of k -dimensional planes having nonempty intersection with a given convex body. This note deals with motion invariant measures on sets… read more here.
Keywords: pairs hyperplanes; geometry; geometry pairs; hyperplanes lines ... See more keywords
Applications of Integral Geometry to Geometric Properties of Sets in the 3D-Heisenberg Group
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DOI: 10.1515/agms-2016-0020
Abstract: Abstract By studying the group of rigid motions, PSH(1), in the 3D-Heisenberg group H1,we define a density and a measure in the set of horizontal lines. We show that the volume of a convex domain… read more here.
Keywords: applications integral; group; heisenberg group; geometry ... See more keywords