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arXiv · 1307.3167

Connectedness properties of the space of complete nonnegatively curved planes

Igor Belegradek·Jing Hu
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Abstract

We study the space of complete Riemannian metrics of nonnegative curvature on the plane equipped with the C^k topology. If k is infinite, we show that the space is homeomorphic to the separable Hilbert space. For any k we prove that the space cannot be made disconnected by removing a finite dimensional subset. A similar result holds for the associated moduli space. The proof combines properties of subharmonic functions with results of infinite dimensional topology and dimension theory. A key step is a characterization of the conformal factors that make the standard Euclidean metric on the plane into a complete metric of nonnegative sectional curvature.

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Igor Belegradek, Jing Hu. 2013-07-11. Connectedness properties of the space of complete nonnegatively curved planes. https://arxiv.org/abs/1307.3167

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