Weakly differentiable mappings between manifolds

On distribution functions of the derivatives of weakly differentiable mappings

Notes on Differentiable Manifolds

Manifolds of Differentiable Densities

We develop a family of infinite-dimensional (i.e. non-parametric) manifolds of probability measures. The latter are defined on underlying Banach spaces, and have densities of class Ck b with respect to appropriate reference measures. The case k = ∞, in which the manifolds are modelled on Fréchet spaces, is included. The manifolds admit the Fisher-Rao metric and the dually flat geometry of Amari...

Mappings of Bounded Distortion Between Complex Manifolds

We obtain Liouville type theorems for holomorphic mappings with bounded s-distortion between Cn and positively curved Kähler manifolds.

Stable Equivalence of Differentiable Manifolds

A natural question, of great generality, various special forms of which are often asked in differential topology, is the following: Let Mi, Mi be differentiable w-manifolds, : M\—»M2 a continuous map which is a homotopy equivalence between M\ and M2. When is there a differentiable isomorphism <3>: Mi—> M2 in the same homotopy class as 0? For example, there is the Poincaré Conjecture which po...