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CHallenges in ANalysis and GEometry between mean and scalar curvature
The interplay between Analysis and Geometry has led to a number of spectacular achievements such as the proof of the Poincaré conjecture by Perelman. The goal of this proposal is to establish a research group that will make striki... The interplay between Analysis and Geometry has led to a number of spectacular achievements such as the proof of the Poincaré conjecture by Perelman. The goal of this proposal is to establish a research group that will make striking progress along the following two directions, that reflect the two souls, extrinsic and intrinsic, of Riemannian Geometry, as well as their mutual interaction. Minimal surfaces, namely surfaces of zero mean curvature, have been an object of mathematical study since the 18th century (with pioneering work by Lagrange and Euler), and yet remain at the heart of many problems to this day. I aim at shading new light on their understanding, by means of a thorough investigation of the Morse index as an observable on the space of minimal cycles, both in general 3-manifolds of positive curvature and in space forms, towards higher Urbano-type theorems and beyond min-max techniques. Partly motivated by the study of data sets for the Einstein equations on the one hand, and by a far-reaching program by Gromov on the other, we also want to systematically study the interplay between the scalar curvature of a manifold and the mean curvature of its boundary. The project, which builds on my recent contributions and long-term experience in the field, relies on a combination of diverse elliptic and parabolic techniques, and aims at developing effective deformation methods that will have a variety of applications. These directions, while seemingly different, are deeply intertwined both at the technical and conceptual level, and incarnate the primary goal of redefining the state of the art in the investigation of infinite-dimensional spaces of solutions to fundamental geometric problems. ver más
28/02/2027
UNITN
1M€
Duración del proyecto: 77 meses Fecha Inicio: 2020-09-14
Fecha Fin: 2027-02-28

Línea de financiación: concedida

El organismo H2020 notifico la concesión del proyecto el día 2020-09-14
Línea de financiación objetivo El proyecto se financió a través de la siguiente ayuda:
ERC-2020-STG: ERC STARTING GRANTS
Cerrada hace 5 años
Presupuesto El presupuesto total del proyecto asciende a 1M€
Líder del proyecto
UNIVERSITA DEGLI STUDI DI TRENTO No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico TRL 4-5