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Geometric and analytic aspects of isoparametric hypersurfaces

Total Cost €


EC-Contrib. €






Project "ISOPARAMETRIC" data sheet

The following table provides information about the project.


Organization address
address: CALLE SERRANO 117
city: MADRID
postcode: 28006

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Spain [ES]
 Project website
 Total cost 158˙121 €
 EC max contribution 158˙121 € (100%)
 Programme 1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
 Code Call H2020-MSCA-IF-2016
 Funding Scheme MSCA-IF-EF-ST
 Starting year 2017
 Duration (year-month-day) from 2017-04-16   to  2019-08-20


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 


 Project objective

Isoparametric hypersurfaces are intriguing geometric objects whose study has revealed connections with several areas of mathematics and mathematical physics, and which have typically been investigated with differential geometric, algebraic or topological techniques.

The aim of this proposal 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.

In order to develop this proposal, the Experienced Researcher will join the Geometric Analysis team at ICMAT, in Madrid, under the supervision of one of its main researchers, Alberto Enciso. The host group has extensive experience in the study of the geometric properties of solutions to differential equations, and their main researchers have recently developed powerful methods to address outstanding problems in fluid mechanics and geometric analysis. The scientific training strategy of this proposal consists in the assimilation of these techniques. On the other hand, the Researcher is experienced in the classical theory of isoparametric hypersurfaces, as evidenced by his contributions to the field. It is the combination of both backgrounds what is needed to develop this proposal.

Finally, this MSC fellowship would boost the convergence of distinct research fields and collaborative networks, produce a synergy with the ERC Starting Grant hold by the Supervisor, diversify the fellow’s mathematical knowledge, and consolidate him as an independent researcher.


year authors and title journal last update
List of publications.
2017 Miguel Domínguez-Vázquez, Alberto Enciso, Daniel Peralta-Salas
Solutions to the overdetermined boundary problem for semilinear equations with position-dependent nonlinearities
published pages: , ISSN: , DOI:
arXiv preprint 2019-09-02
2018 José Carlos Díaz-Ramos, Miguel Domínguez-Vázquez, Cristina Vidal-Castiñeira
Isoparametric submanifolds in two-dimensional complex space forms
published pages: 205-216, ISSN: 0232-704X, DOI: 10.1007/s10455-017-9572-2
Annals of Global Analysis and Geometry 53/2 2019-09-02
2017 José Carlos Díaz-Ramos, Miguel Domínguez-Vázquez, Víctor Sanmartín-López
Anti-De Sitter spacetimes and isoparametric hypersurfaces in complex space forms
published pages: , ISSN: , DOI: 10.1007/978-3-319-66290-9
Lorentzian Geometry and Related Topics 211 2019-09-02
2018 José Carlos Díaz-Ramos, Miguel Domínguez-Vázquez, Andreas Kollross
On homogeneous manifolds whose isotropy actions are polar
published pages: 1-20, ISSN: 0025-2611, DOI: 10.1007/s00229-018-1077-1
manuscripta mathematica 2019-09-02
2018 Miguel Domínguez-Vázquez, Claudio Gorodski
Polar foliations on quaternionic projective spaces
published pages: 353-375, ISSN: 0040-8735, DOI: 10.2748/tmj/1537495351
Tohoku Mathematical Journal 70/3 2019-09-02
2018 Dominguez-Vazquez, Miguel; Perez-Barral, Olga
Ruled hypersurfaces with constant mean curvature in complex space forms
published pages: 1-7, ISSN: , DOI:
arXiv preprint 1 2019-09-02
2018 Domínguez-Vázquez, Miguel; Manzano, José M.
Isoparametric surfaces in $mathbb{E}(kappa,tau)$-spaces
published pages: 1-13, ISSN: , DOI:
arXiv preprint 1 2019-09-02
2018 José Carlos Díaz-Ramos, Miguel Domínguez-Vázquez, Cristina Vidal-Castiñeira
Strongly 2-Hopf hypersurfaces in complex projective and hyperbolic planes
published pages: 469-486, ISSN: 0373-3114, DOI: 10.1007/s10231-017-0687-7
Annali di Matematica Pura ed Applicata (1923 -) 197/2 2019-09-02
2019 J. Carlos Díaz-Ramos, Miguel Domínguez-Vázquez, Víctor Sanmartín-López
Submanifold geometry in symmetric spaces of noncompact type
published pages: , ISSN: 2316-9028, DOI: 10.1007/s40863-019-00119-6
São Paulo Journal of Mathematical Sciences 2019-09-02
2017 José Carlos Díaz-Ramos, Miguel Domínguez-Vázquez, Víctor Sanmartín-López
Isoparametric hypersurfaces in complex hyperbolic spaces
published pages: 756-805, ISSN: 0001-8708, DOI: 10.1016/j.aim.2017.05.012
Advances in Mathematics 314 2019-09-02

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