Counter-intuitive existence and approximation results
– Raum 0.14
We will discuss a general approximation theorem which allows to solve overdetermined partial differential relations on an open dense subset of the domain. Let K be a real number. Applications will show that
- Every C1-function can be uniformly approximated by Lipschitz functions with derivative = K on an open dense subset;
- Every embedding of a surface in R3 can be C1-approximated by embeddings with Gauss curvature = K on an open dense subset;
- Every manifold of dimension at least 2 has a C1,1-metric which is smooth and has constant sectional curvature K on an open dense subset.
This is joint work with Bernhard Hanke (Augsburg).