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Geometric and analytic aspects of isoparametric hypersurfaces

Acronym: ISOPARAMETRIC.

Scientist in charge: Alberto Enciso Carrasco.

Experienced Researcher: Miguel Domínguez Vázquez

Project Reference: 745722

Start Date: 2017-04-16

End Date: 2019-04-15

Abstract:

Isoparametric hypersurfaces are intriguing geometric objects whose study traces back to works of É. Cartan, B. Segre and T. Levi-Civita in the 30s. Over the last few decades, the investigation of these objects, typically carried out by means of differential geometric, algebraic or topological techniques, has revealed connections with several areas of mathematics and mathematical physics.

The aim of this project is to develop an innovative approach to isoparametric hypersurfaces by combining already established tools with methods from geometric analysis and partial differential equations. Specifically, we intend to investigate the existence of isoparametric hypersurfaces in general Riemannian manifolds, the role of these objects in overdetermined problems of elliptic partial differential equations, and the isoparametricity of compact hypersurfaces with constant mean curvature in noncompact symmetric spaces.

 

Bandera UE

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 745722.