In the talk I will discuss the following result and related analytic and geometric questions: On the boundary of any convex body in the Euclidean space there exists at least one infinite geodesic.
We will present a somewhat different proof of Agol's theorem that
3-manifolds
with RFRS fundamental group admit a finite cover which fibers over S^1.
This is joint work with Takahiro Kitayama.
Let gamma be a closed knotted curve in R^3 such that the tubular
neighborhood U_r (gamma) with given radius r>0 does not intersect
itself. The length minimizing curve gamma_0 within a prescribed knot class is
called ideal knot. We use a special representation of curves and tools from
nonsmooth analysis to derive a characterization of ideal knots. Analogous
methods can be used for the treatment of self contact of elastic rods.