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arXiv · 1510.05777

Compactness theorems for the spaces of distance measure spaces and Riemann surface laminations

Divakaran Divakaran·Siddhartha Gadgil
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Abstract

In this paper, we give a generalisation of Gromov's compactness theorem for metric spaces, more precisely, we give a compactness theorem for the space of distance measure spaces equipped with a \emph{generalised Gromov-Hausdorff-Levi-Prokhorov distance}. Using this result we prove that the Deligne-Mumford compactification is the completion of the moduli space of Riemann surfaces under the generalised Gromov-Hausdorff-Levi-Prokhorov distance. Further we prove a compactness theorem for the space of Riemann surface laminations.

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Divakaran Divakaran, Siddhartha Gadgil. 2015-10-20. Compactness theorems for the spaces of distance measure spaces and Riemann surface laminations. https://arxiv.org/abs/1510.05777

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