Applications of Integral Geometry to Geometric Properties of Sets in the 3D-Heisenberg Group
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 D ⊂ H1 is equal to the integral of the length of chords of all horizontal lines intersecting D. As in classical i...
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| Format: | Article |
| Language: | English |
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De Gruyter
2017-01-01
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| Series: | Analysis and Geometry in Metric Spaces |
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| Online Access: | https://doi.org/10.1515/agms-2016-0020 |