Isoperimetric regions in H^2 between parallel horocycles
Marcio Fabiano da Silva
TL;DR
This paper solves the isoperimetric problem in the hyperbolic plane between two parallel horocycles, explicitly characterizing all regions of minimal perimeter for a given area.
Contribution
It provides a detailed and explicit description of isoperimetric regions in hyperbolic geometry between parallel horocycles, advancing understanding of geometric optimization in non-Euclidean spaces.
Findings
Explicit characterization of isoperimetric regions between horocycles
Complete description of minimal perimeter regions for prescribed areas
Advancement in hyperbolic geometric analysis
Abstract
In this work we investigate the following isoperimetric problem in the hyperbolic plane: to find the regions of prescribed area with minimal perimeter between two parallel horocycles. We give an explicit and detailed description of all such regions.
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Taxonomy
TopicsMathematics and Applications · Geometric and Algebraic Topology · Mathematical Dynamics and Fractals