We study systems that are monotone in a generalized sense with respect to cones of rank 2. The main result of the paper is the existence of a Poincaré-Bendixson property for some solutions of those systems.

Abstract. We prove a compact embedding theorem in a class of spaces of piecewise H functions subordinated to a class of shape regular, but not necessarily quasi-uniform triangulations of a polygonal domain. This result generalizes the Rellich–Kondrachov theorem. It is used to prove generalizations to piecewise functions of nonstandard Poincaré–Friedrichs inequalities. It can be used to prove Ko...

We consider the reduction of supersymmetry in N -extended four dimensional supergravity via the super Higgs mechanism. We provide an analysis largely based on the properties of long and short multiplets of Poincaré supersymmetry. Examples of the super Higgs phenomenon are realized in spontaneously broken N = 8 supergravity through the Scherk-Schwarz mechanism and in superstring compactification...

We consider the 2D Poincaré gravity and show its exact integrability. The choice of the gauge is discussed. The Euclidean solutions on compact closed differential manifolds are studied. ∗ e-mail: [email protected]

LetΩ be aC2+γ domain in RN ,N ≥ 2, 0 < γ < 1. LetT>0 and let L be a uniformly parabolic operator Lu= ∂u/∂t−∑i, j(∂/∂xi)(ai j(∂u/∂xj)) +∑ j b j(∂u/∂xi) + a0u, a0 ≥ 0, whose coefficients, depending on (x, t) ∈Ω×R, are T periodic in t and satisfy some regularity assumptions. Let A be the N ×N matrix whose i, j entry is ai j and let ν be the unit exterior normal to ∂Ω. Let m be a T-periodic functio...

We show that certain 5d, N = 2 Yang-Mills/Einstein supergravity theories admit the gauging of the full R-symmetry group, SU(2)R, of the underlying N = 2 Poincaré superalgebra. This generalizes the previously studied Abelian gaugings of U(1)R ⊂ SU(2)R, and completes the construction of the most general vector and tensor field coupled 5d, N = 2 supergravity theories with gauge interactions. The g...

The principal result of this paper is an explicit description of the structure of ramification subgroups of the Galois group of 2-dimensional local field modulo its subgroup of commutators of order ≥ 3. This result plays a clue role in the author’s proof of an analogue of the Grothendieck Conjecture for higher dimensional local fields, cf. Proc. Steklov Math. Institute, vol. 241, 2003, pp. 2-34.

We show that certain five-dimensional, N = 2 Yang-Mills/Einstein supergravity theories admit the gauging of the full R-symmetry group, SU(2)R, of the underlying N = 2 Poincaré superalgebra. This generalizes the previously studied Abelian gaugings of U(1)R ⊂ SU(2)R, and completes the construction of the most general vector and tensor field coupled five-dimensional,N = 2 supergravity theories wit...

For a large class of word hyperbolic groups Γ the cross product C∗-algebras C(∂Γ)⋊Γ, where ∂Γ denotes the Gromov boundary of Γ satisfy Poincaré duality in K-theory. This class strictly contains fundamental groups of compact, negatively curved manifolds. We discuss the general notion of Poincaré duality for C∗-algebras, construct the fundamental classes for the aforementioned algebras, and prove...

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...