The Calderon problem for two-dimensional manifolds by the BC-method (a corrected version) As was shown by M.Lassas and G.Uhlmann (2001), the smooth two-dimensional compact orientable Riemann manifold with the boundary is uniquely determined by its Dirichlet-to-Neumann map up to conformal equivalence. We give a new proof of this fact based on relations between the Calderon problem and Function A...

We consider closed topological 4-manifolds M with universal cover S × S and Euler characteristic χ(M) = 1. All such manifolds with π = π1(M) ∼= Z/4 are homotopy equivalent. In this case, we show that there are four homeomorphism types, and propose a candidate for a smooth example which is not homeomorphic to the geometric quotient. If π ∼= Z/2×Z/2, we show that there are three homotopy types (a...

We compute the divisor of Selberg's zeta function for convex co-compact, torsion-free discrete groups acting on a real hyperbolic space of dimension n + 1. The divisor is determined by the eigenvalues and scattering poles of the Laplacian on X = nH together with the Euler characteristic of X compacti ed to a manifold with boundary. If n is even, the singularities of the zeta funciton associated...

We prove that any asymptotically locally Euclidean scalar-flat Kähler 4-orbifold whose isometry group contains a 2-torus is isometric, up to an orbifold covering, to a quaternionic-complex quotient of a k-dimensional quaternionic vector space by a (k − 1)-torus. In order to do so, we first prove that any compact anti-self-dual 4-orbifold with positive Euler characteristic whose isometry group c...

We prove that the homotopy class of a Morin mapping f : P p → Q with p − q odd contains a cusp mapping. This affirmatively solves a strengthened version of the Chess conjecture [5],[3]. Also, in view of the Saeki-Sakuma theorem [10] on the Hopf invariant one problem and Morin mappings, this implies that a manifold P p with odd Euler characteristic does not admit Morin mappings into R for p ≥ 2k...

The (d,1)-total labelling of graphs was introduced by Havet and Yu. In this paper, we consider the list version of (d,1)-total labelling of graphs. Let G be a graph embedded in a surface with Euler characteristic ε whose maximum degree ∆(G) is sufficiently large. We prove that the (d,1)-total choosability C d,1(G) of G is at most ∆(G) + 2d.

In this note we reconsider the continuous time limit of the GARCH(1, 1) process. Let > k and p2 k denote, respectively, the cumulative returns and the volatility processes. We consider the continuous time approximation of the couple (> k , p2 k ). We show that, by choosing di!erent parameterizations, as a function of the discrete interval h, we can obtain either a degenerate or a non-degenerate...