Joergen Olsen Lye
My personal webpage
Projects & Papers
Ongoing Projects
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Yamabe Flow. This is a smaller project investigating Yamabe-like flows. Joint with Boris Vertman and Mannaim Vitti.
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Geodesics under metric degeneration. We study the behaviour of the geodesics as a Riemannian metric degenerates to a conical or cuspidal metric. Joint with Daniel Grieser.
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Non-compact examples of Ricci-flat metrics. We are trying to find more Ricci-flat metrics using Calabi's construction. This will be joint with Roger Bielawski.
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Constructing Quaternion-Kähler manifolds. We are trying to construct more examples of complete quaternion-Kähler manifold, for instance by resolutions of orbifolds. Joint with Lothar Schiemanowski.
Papers and Preprints
Stable geodesics on a K3 surface (unpublished PhD thesis).
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Geodesics on a K3 Surface near the Orbifold Limit. This is an extension and a summary of my PhD thesis.
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Geodesics Orbiting a Singularity. Joint with Daniel Grieser.
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Convergence of the Yamabe flow on singular spaces with positive Yamabe constant (accepted for publication by Tohoku Mathematical Journal). Joint with Gilles Carron and Boris Vertman.
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A detailed look at the Calabi-Eguchi-Hanson spaces (preprint).
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Long-time existence of Yamabe flow on singular spaces with positive Yamabe constant. Joint with Boris Vertman.
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Analytic torsion for fibred boundary metrics and conic degeneration (preprint). Joint with Boris Vertman.