Ricci flow from spaces with edge type conical singularities

Lead Research Organisation: University of Warwick
Department Name: Mathematics


Ricci Flow has seen been a tool in recent breakthroughs in the EPSRC research area of 'Geometry and Topology': It was fundamental in the proof of the Poincaré and Geometrization Conjectures, the Differentiable Sphere Theorem, the proof of the Anderson-Cheeger-Colding-Tian conjecture in dimension three, and the Generalized Smale Conjecture. In work of M. Simon and P. Topping on the proof of the Anderson-Cheeger-Colding-Tian conjecture in dimension three, Ricci Flow was used to smooth out Ricci limit spaces. A further open question in this direction is if Ricci Flow can be used to smooth out positively curved polyhedral spaces in higher dimension. First steps in this direction have recently been achieved by Bamler-Cabezas-Rivas-Wilking and Gianniotis-Schulze with different approaches. The work of Gianniotis-Schulze shows that it possible to construct a Ricci Flow starting from a compact manifold with isolated conical singularities which are modelled on positively curved cones. As a first step towards flowing from polyhedral spaces, Lucas Lavoyer de Miranda is working on extending the results of Gianniotis-Schulze to the case that the conical singularities occur along a closed curve. There are several new ideas and techniques to be developed. Successful completion of this project will be fundamental in developing an approach to flowing from positively curved polyhedral spaces.


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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/V520226/1 30/09/2020 31/10/2025
2443749 Studentship EP/V520226/1 04/10/2020 04/10/2024 Lucas LAVOYER DE MIRANDA