On the Gromov-Hausdorff Limits of Compact Surfaces with Boundary
Metric Geometry
2024-07-03 v1 Differential Geometry
Abstract
In this work we investigate Gromov-Hausdorff limits of compact surfaces carrying length metrics. More precisely, we consider the case where all surfaces have the same Euler characteristic. We give a complete description of the limit spaces and study their topological properties. Our investigation builds on the results of a previous work which treats the case of closed surfaces.
Keywords
Cite
@article{arxiv.2407.01642,
title = {On the Gromov-Hausdorff Limits of Compact Surfaces with Boundary},
author = {Tobias Dott},
journal= {arXiv preprint arXiv:2407.01642},
year = {2024}
}
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27 pages