We consider natural conformal invariants arising from the Gauss-Bonnet formulas on manifolds with boundary, and study conformal deformation problems associated to them. The purpose of this paper is to study conformal deformation problems associated to conformal invariants on manifolds with boundary. From analysis point of view, the problem becomes a non-Dirichlet boundary value problems for ful...

We study the “conformal groups” of Jordan algebras along the lines suggested by Kantor. They provide a natural generalization of the concept of conformal transformations that leave 2-angles invariant to spaces where “p-angles” (p ≥ 2) can be defined. We give an oscillator realization of the generalized conformal groups of Jordan algebras and Jordan triple systems. A complete list of the general...

We consider random dynamical systems such as groups of conformal transformations with a probability measure, or transversaly conformal foliations with a Laplace operator along the leaves, in which case we consider the holonomy pseudo-group. We prove that either there exists a measure invariant under all the elements of the group (or the pseudo-group), or almost surely a long composition of maps...

Dynamical symmetries of the collisionless Boltzmann transport equation, or Vlasov equation, but under the influence of an external driving force, are derived from non-standard representations of the 2D conformal algebra. In the case without external forces, the symmetry of the conformally-invariant transport equation is first generalized by considering the particle momentum as an independent va...

Using the duality equations of Moore and Seiberg we define for every primary field in a Rational Conformal Field Theory a proper Markov trace and hence a knot invariant. Next we define two nested algebras and show, using results of Ocneanu, how the position of the smaller algebra in the larger one reproduces part of the duality data. A new method for constructing Rational Conformal Field Theori...

We study invariant measures and thermodynamic formalism for a class of endomorphisms FT which are only piecewise differentiable on countably many pieces non-conformal. The endomorphism has random generated limit sets JT,ω in stable fibers. prove Global Volume Lemma implying that the projections equilibrium exact dimensional non-compact global basic set JT. A dimension formula these is obtained ...