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...
Main Author: | Huang Yen-Chang |
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Format: | Article |
Language: | English |
Published: |
De Gruyter
2017-01-01
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Series: | Analysis and Geometry in Metric Spaces |
Subjects: | |
Online Access: | https://doi.org/10.1515/agms-2016-0020 |
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