Final Activity Report Summary - NADITIDIBAS (Nonlinear analysis and differential topology in infinite dimensional Banach spaces)
As a result of this project the following were achieved:
A new maximum principle was obtained for viscosity subsolutions and supersolutions of evolution equations on a Riemannian manifold with some weak restrictions.
A new notion of proximal gradient was introduced for functions defined on Riemannian manifold and a nonsmooth calculus (in the sense of Clarke) was developed for this new notion.
Several new fixed point theorems were obtained, concerning expansive and nonexpansive mappings on a (possibly non compact) Riemannian manifold and their small perturbations.
New regularisation results were obtained for convex functions defined on Riemannian manifolds with negative sectional curvature (by generalizing Moreau's inf-convolution procedure in this context).
A new maximum principle was obtained for viscosity subsolutions and supersolutions of evolution equations on a Riemannian manifold with some weak restrictions.
A new notion of proximal gradient was introduced for functions defined on Riemannian manifold and a nonsmooth calculus (in the sense of Clarke) was developed for this new notion.
Several new fixed point theorems were obtained, concerning expansive and nonexpansive mappings on a (possibly non compact) Riemannian manifold and their small perturbations.
New regularisation results were obtained for convex functions defined on Riemannian manifolds with negative sectional curvature (by generalizing Moreau's inf-convolution procedure in this context).