p-dimensional cones and applications

We introduce a notion of p-dimensional cones made of $p$-dimensional subspaces and gauges on these cones, giving rise to a contraction principle which generalizes the one for Birkhoff cones. Using tools on the grassmannian and the exterior algebra, we prove a spectral gap result for the p largest eigenvalues of an operator and a regularity result for the characteristic exponents of a random product of cone-contracting operators.