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EU-Förderung (2.412.795 €): Generic regularity of area minimising hypersurfaces and mean curvature flows Hor30.09.2025 EU-Rahmenprogramm für Forschung und Innovation "Horizont"
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Generic regularity of area minimising hypersurfaces and mean curvature flows
Major advances in geometry and topology have been achieved by studying critical points and gradient flows for natural energies, but these analytic methods are hindered when singularities occur. In fact, singularities are the main obstacle in the use of area minimisation in the proof of the positive mass theorem up to dimension 7 and the use of Ricci flow with surgery in the proof of the 3-dimensional Poincaré conjecture. A key observation in geometry and physics is that generic solutions, obtained by small perturbations, can exhibit simpler singularities or even none at all. This phenomenon, called generic regularity, can yield outstanding results. The recent generic regularity breakthroughs by the PI-led group will allow to address fundamental open problems in three areas: For area-minimising hypersurfaces, we aim to extend generic regularity to all dimensions, building on the PI's work in up to 10 dimensions. This would establish the positive mass theorem in all dimensions, bypassing technical analysis of the singular set of minimisers. It would also allow the resolution of other well-known problems related to scalar curvature. For mean curvature flow singularities, which are unavoidable, generic flows are expected to encounter only the simplest types. Work of the PI has proven this in 3 and 4 dimensions up to the problem of “multiplicity”. Bamler–Kleiner recently excluded multiplicity in 3 dimensions. Our goal is to prove that multiplicity generically cannot occur in higher dimensions. This would mark major progress towards the Schoenflies conjecture, a main open problem in 4-dimensional topology. For special Lagrangian submanifolds, fundamental objects in symplectic geometry, we would geometrise Lagrangians in Calabi-Yau manifolds by establishing generic Lagrangian mean curvature flows through singularities. The anticipated contributions to mirror symmetry are expected to impact fields spanning algebra, geometry, topology, and theoretical physics.
Geförderte Unternehmen:
| Firmenname | Förderungssumme |
| University of Warwick | 2.412.795 € |
Quelle: https://cordis.europa.eu/project/id/101200301
Diese Bekanntmachung wurde von Englisch nach Deutsch übersetzt. Die Bekanntmachung bezieht sich auf einen vergangenen Zeitpunkt, und spiegelt nicht notwendigerweise den heutigen Stand wider. Der aktuelle Stand wird auf folgender Seite wiedergegeben: University of Warwick, Coventry, Großbritannien.
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