. We show that given a quasi-circle C in partial derivative infinity H3 (respectively in partial derivative infinity ADS3) and a complete conformal metric h on D whose curvature Kh takes values in a compact subset of (-1, 0) (respectively (-infinity, -1)), with all derivatives bounded with respect to the hyperbolic metric, there exists a smooth that V extends continuously to a homeomorphism partial derivative V : S1 -* C. In the case of hyperbolic space, the statement still holds if C is a Jordan curve.
. In this paper, we study Schwarz-Pick estimates for high order Frechet derivatives of bounded holomorphic mappings on classical domains of type (I)-(IV) in matrix-spaces described in the original paper of E. Cartan. Our first aim is to give Schwarz-Pick type estimates for holomorphic functions from classical domains into bounded convex domains in C. The second aim is to give such estimates for Frechet derivatives of holomorphic self-mappings on classical domains.
We show that if an endomorphism f : T2 -> T2 is absolutely partially hyperbolic, then it has a center foliation. Moreover, the center foliation is leaf conjugate to that of its linearization.
We give a family of examples of discrete Schro & uml;dinger operators whose spectral dimension is not invariant under sieving. The examples are produced from the Fibonacci Hamiltonian, which is one of the main models of a one-dimensional quasicrystal. We also give a family of examples in which the local Hausdorff dimension tends to zero in some parts of the spectrum as the sieving parameter is sent to infinity.
. In this note, we consider the optimal transportation with symmetries. We prove that if a cost function and marginal measures are invariant under a homeomorphism group G, which is a product of a compact factor and an abelian group, then a solution of the Monge-Kantorovich problem is G-invariant. This extends the works of Klein-Kramer-Noe [Equivariant flow ran Associates, Inc., 2023] from compact groups and of Moameni [Discrete Contin. Dyn. Syst. 36 (2016), pp. 2653-2671] for an abelian group.
