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The Klingenberg-Sakai conjecture and the space of positively pinched metrics

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Moduli Spaces of Riemannian Metrics

Part of the book series: Oberwolfach Seminars ((OWS,volume 46))

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Abstract

As a sort of epilogue to the preceding parts of this book, we will discuss a conjecture of Klingenberg and Sakai in positive sectional curvature, concerning the existence of lower uniform bounds for the injectivity radius of δ-pinched metrics on manifolds in terms of the manifold and the pinching constant.

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Tuschmann, W., Wraith, D.J. (2015). The Klingenberg-Sakai conjecture and the space of positively pinched metrics. In: Moduli Spaces of Riemannian Metrics. Oberwolfach Seminars, vol 46. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0948-1_11

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