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Mikhail Gromov - 1/4 Old, New and Unknown around Scalar Curvature




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Название :  Mikhail Gromov - 1/4 Old, New and Unknown around Scalar Curvature
Продолжительность :   6579
Пользователь :  Institut des Hautes Études Scientifiques (IHÉS)
Дата публикации :   2019-02-16
Просмотры :   5,673
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Geometry of scalar curvature, that is comparable in scope to symplectic geometry, mediates between two worlds: the domain of rigidity, one sees in convexity and the realm of softness, characteristic of topology, such as the cobordism theory.

The aim of this course is threefold:

1. An overview of old and new results, mostly, but not exclusively, on the rigidity side, of manifolds X with positive and, more generally, bounded from below scalar curvatures Sc(X), along with a brief introduction to main techniques.

2. Proof of new geometric comparison type inequalities for Riemannian manifolds X with lower bounds on Sc(X) and on mean curvatures of the boundaries of X.

3. Discussion of open problems concerning Sc superior at 0.


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