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Horizontal curves of hyperbolic metrics
Melanie Rupflin1, Peter M Topping2
11Mathematical Institute, University of Oxford, Oxford, OX2 6GG UK.
Calculus of Variations and Partial Differential Equations
|April 12, 2019
Summary
This study analyzes hyperbolic metrics moving horizontally, revealing fine convergence properties. These findings are relevant for understanding metric spaces and harmonic maps in geometric analysis.
Area of Science:
- Differential Geometry
- Geometric Analysis
Background:
- Hyperbolic metrics are fundamental in geometry and analysis.
- Understanding their behavior under continuous transformations is crucial.
Purpose of the Study:
- To analyze the fine convergence properties of one-parameter families of hyperbolic metrics.
- To investigate metrics moving horizontally, orthogonal to diffeomorphisms.
Main Methods:
- Analysis of one-parameter families of hyperbolic metrics.
- Investigating horizontal movement and its implications for convergence.
Main Results:
- Detailed characterization of the convergence properties of these specific metric families.
- Demonstration of how horizontal movement influences metric convergence.
Conclusions:
- The study provides insights into the behavior of hyperbolic metrics under specific transformations.
- Findings contribute to the theory of curves of metrics and harmonic map flows.
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