The existence of horizontal envelopes in the 3D-Heisenberg group
Yen-Chang Huang
TL;DR
This paper investigates the conditions under which horizontal envelopes exist in the 3D-Heisenberg group, providing a classification and a construction method for such envelopes.
Contribution
It establishes necessary and sufficient conditions for horizontal envelopes in the 3D-Heisenberg group and introduces a method for their construction and classification.
Findings
Derived necessary and sufficient conditions for horizontal envelopes.
Developed a method to construct horizontal envelopes from given data.
Classified solutions satisfying the construction criteria.
Abstract
By using the support function on the -plane, we show the necessary and sufficient conditions for the existence of envelopes of horizontal lines in the 3D-Heisenberg group. A method to construct horizontal envelopes from the given ones is also derived, and we classify the solutions satisfying the construction.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Point processes and geometric inequalities · Advanced Numerical Analysis Techniques