Geodesics in the Heisenberg Group

LIPSCHITZ ESTIMATES FOR GEODESICS IN THE HEISENBERG GROUP by

Absolute Continuity of Wasserstein Geodesics in the Heisenberg Group

In this paper we answer to a question raised by Ambrosio and Rigot [2] proving that any interior point of a Wasserstein geodesic in the Heisenberg group is absolutely continuous if one of the end-points is. Since our proof relies on the validity of the so-called Measure Contraction Property and on the fact that the optimal transport map exists and the Wasserstein geodesic is unique, the absolut...

Geodesics on the Symplectomorphism Group

In [E-M] we proved the existence of geodesics for a right invariant L Riemannian metric on the group of volume preserving diffeomorphisms (volumorphisms) of a compact manifold M. These geodesics are important because they describe all possible motions of an incompressible inviscid fluid which fills M. In the present work we shall assume that M has a symplectic form ω and prove the same result f...

The Heisenberg Group Fourier Transform

1. Fourier transform on Rn 1 2. Fourier analysis on the Heisenberg group 2 2.1. Representations of the Heisenberg group 2 2.2. Group Fourier transform 3 2.3. Convolution and twisted convolution 5 3. Hermite and Laguerre functions 6 3.1. Hermite polynomials 6 3.2. Laguerre polynomials 9 3.3. Special Hermite functions 9 4. Group Fourier transform of radial functions on the Heisenberg group 12 Ref...

Isometry-invariant geodesics and the fundamental group

We prove that on closed Riemannian manifolds with infinite abelian, but not cyclic, fundamental group, any isometry that is homotopic to the identity possesses infinitely many invariant geodesics. We conjecture that the result remains true if the fundamental group is infinite cyclic. We also formulate a generalization of the isometry-invariant geodesics problem, and a generalization of the cele...