| Abstract: |
| Maximum principles at infinity (or almost maximum principles), such as for instance Ekeland and Omori-Yau principles, are a powerful tool to investigate the geometry of Riemannian manifolds. Their validity is intimately related to the geometry of the underlying space, and exhibit deep relations with the theory of stochastic processes and to potential theory. In the first part of the talk, I will present a survey of a few geometric applications to motivate the study of these principles, and discuss their link with probability. Then, I will discuss a recent underlying duality with the existence of suitable exhaustion functions called Khas`minskii potentials. Indeed, duality holds for a broad class of fully-nonlinear operators of geometric interest.
This is based on joint works with B. Bianchini, M. Rigoli, P. Pucci, D. Valtorta and L. F. Pessoa. |
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