On geodesic homotopies of controlled width and conjugacies in isometry groups. (English) Zbl 1435.53032
Summary: We give an analytical proof of the Poincaré-type inequalities for widths of geodesic homotopies between equivariant maps valued in Hadamard metric spaces. As an application we obtain a linear bound for the length of an element conjugating two finite lists in a group acting on an Hadamard space.
MSC:
| 53C23 | Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces |
| 58E20 | Harmonic maps, etc. |
| 20F65 | Geometric group theory |
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