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arXiv · 2407.01642

On the Gromov-Hausdorff Limits of Compact Surfaces with Boundary

Tobias Dott
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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.

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Tobias Dott. 2024-06-30. On the Gromov-Hausdorff Limits of Compact Surfaces with Boundary. https://arxiv.org/abs/2407.01642

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