Non-existence of geometric minimal foliations in hyperbolic three-manifolds

期刊： COMMENTARII MATHEMATICI HELVETICI, 2020; 95 (1)

We show that every three-dimensional hyperbolic manifold admits no locally geometric 1-parameter family of closed minimal surfaces. Here such a geomet......

Fractal geometry of the complement of Lagrange spectrum in Markov spectrum

期刊： COMMENTARII MATHEMATICI HELVETICI, 2020; 95 (3)

The Lagrange and Markov spectra are classical objects in Number Theory related to certain Diophantine approximation problems. Geometrically, they are ......

Rigidity of center Lyapunov exponents and su-integrability

期刊： COMMENTARII MATHEMATICI HELVETICI, 2020; 95 (3)

Let f be a conservative partially hyperbolic diffeomorphism, which is homotopic to an Anosov automorphism A on T-3. We show that the stable and unstab......

Transverse foliations on the torus T-2 and partially hyperbolic diffeomorphisms on 3-manifolds

期刊： COMMENTARII MATHEMATICI HELVETICI, 2017; 92 (3)

In this paper, we prove that given two C-1 foliations F and G on T-2 which are transverse, there exists a non-null homotopic loop {Phi(t)}t is an elem......

JIF：0.92