Sep 20 – 22, 2023
Le Bois-Marie
Europe/Paris timezone

Variants of Lojasiewicz's gradient inequality

Sep 22, 2023, 10:00 AM
Centre de conférences Marilyn et James Simons (Le Bois-Marie)

Centre de conférences Marilyn et James Simons

Le Bois-Marie

35, route de Chartres 91440 Bures-sur-Yvette


Prof. Krzysztof Kurdyka (Univ. Savoie Mont Blanc)


The celebrated Lojasiewicz gradient inequality (L) has an important consequence; the length of a gradient trajectory, between two levels, is uniformly bounded. So, a trajectory has a limit when approaching a critical level. It has inspired Ren ́e Thom to formulate the conjecture that the trajectory has a tangent at the limit.

I will describe various versions and extensions of inequality (L). I will state a variant of this inequality, which is valid for a map with values in a finite-dimensional vector space. It yields the boundedness of the volume of a submanifold transverse to the kernels of differentials of the map. This is an analogue of the boundedness of the length of gradient trajectories.

Presentation materials