Cours de l'IHES 2018-2019

Old, New and Unknown around Scalar Curvature (4/4)

by Prof. Mikhail Gromov (IHES)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures sur Yvette

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>0.

From the same series
1 2 3
Organized by

Emmanuel Ullmo & Pierre Pansu