Bloch Constants and Bloch Minimal Surfaces

Bloch Constants of Bounded Symmetric Domains

Let D1 and D2 be two irreducible bounded symmetric domains in the complex spaces V1 and V2 respectively. Let E be the Euclidean metric on V2 and h the Bergman metric on V1. The Bloch constant b(D1,D2) is defined to be the supremum of E(f ′(z)x, f ′(z)x) 1 2 /hz(x, x)1/2, taken over all the holomorphic functions f : D1 → D2 and z ∈ D1, and nonzero vectors x ∈ V1. We find the constants for all th...

Triviality of Bloch and Bloch-Dirac bundles

In the framework of the theory of an electron in a periodic potential, we reconsider the longstanding problem of the existence of smooth and periodic quasi-Bloch functions, which is shown to be equivalent to the triviality of the Bloch bundle. By exploiting the time-reversal symmetry of the Hamiltonian and some bundle-theoretic methods, we show that the problem has a positive answer in any dime...

Accumulation constants of iterated function systems with Bloch target domains

The sequence {Fn} is called the iterated function system coming from the sequence f1, f2, f3, . . .; we abbreviate this to IFS. By Montel’s theorem (see for example [3]), the sequence Fn is a normal family, and every convergent subsequence converges uniformly on compact subsets of ∆ to a holomorphic function F . The limit functions F are called accumulation points. Therefore every accumulation ...

Bloch Brane

We investigate a system described by two real scalar fields coupled with gravity in (4, 1) dimensions in warped spacetime involving one extra dimension. The results show that the parameter which controls the way the two scalar fields interact induces the appearence of thick brane which engenders internal structure, driving the energy density to localize inside the brane in a very specific way.

Bloch equations_FF