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Tobias Dott

Publications and source records attributed to Tobias Dott.

3 recordsLinked to original sources
arXiv2025

Convergence of Riemannian 2-manifolds under a uniform curvature and contractibility bound

We consider uniformly semi-locally 1-connected sequences of closed connected Riemannian 2-manifolds. In particular, we assume that the manifolds are homeomorphic to each other and that their total absolute curvature is uniformly bounded. The purpose of this paper is a description of the Gromov-Hausdorff limits of such sequences. Our work extends earlier investigations by Burago and Shioya.

math.MG↗
arXiv2024

On the Gromov-Hausdorff Limits of Compact Surfaces with Boundary

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.

math.MG↗