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Stability of Ricci de Turck flow on singular spaces

  • Klaus KrönckeEmail author
  • Boris Vertman
Article

Abstract

In this paper we establish stability of the Ricci de Turck flow near Ricci-flat metrics with isolated conical singularities. More precisely, we construct a Ricci de Turck flow which starts sufficiently close to a Ricci-flat metric with isolated conical singularities and converges to a singular Ricci-flat metric under an assumption of integrability, linear and tangential stability. We provide a characterization of conical singularities satisfying tangential stability and discuss examples where the integrability condition is satisfied.

Mathematics Subject Classification

Primary 53C44 Secondary 53C25 58J35 

Notes

Acknowledgements

The second author thanks Jan Swoboda for important discussions about aspects of Ricci flow. Both authors thank the Geometry at Infinity Priority program of the German Research Foundation DFG for its financial support and for providing a platform for joint research. The authors greatfully acknowledge hospitality of the Mathematical Institutes at Hamburg and Oldenburg Universities.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.University HamburgHamburgGermany
  2. 2.Universität OldenburgOldenburgGermany

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