The mechanism of gravitational baryogenesis, based on the CPT -violating gravitational interaction between the derivative of the Ricci scalar curvature and the baryon-number current, is investigated in the context of the Gauss-Bonnet braneworld cosmology. We study the constraints on the fundamental five-dimensional gravity scale, the effective scale of B-violation and the decoupling temperature...

We prove that the Atiyah-Singer Dirac operator / Dg in L 2 depends Riesz continuously on L∞ perturbations of complete metrics g on a smooth manifold. The Lipschitz bound for the map g → / Dg(1 + / D 2 g) − 12 depends on bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius. Our proof uses harmonic analysis techniques related to Calderón’s first commu...

Using Fefferman’s classical result on the boundary singularity of the Bergman kernel, we give an analogous description of the boundary behaviour of various related quantities like the Bergman invariant, the coefficients of the Bergman metric, of the associated Laplace-Beltrami operator, of its curvature tensor, Ricci curvature and scalar curvature. The main point is that even though one would e...

Abstract Torsion free connections and a notion of curvature are introduced on the infinite dimensional nonlinear configuration space Γ of a Riemannian manifold M under a Poisson measure. This allows to state identities of Weitzenböck type and energy identities for anticipating stochastic integral operators. The one-dimensional Poisson case itself gives rise to a non-trivial geometry, a de Rham-...

Let M be an orientable connected and compact real hypersurface of the complex space form C(n+1)/2. If the mean curvature α and the function f = g(Aξ, ξ) of hypersurface M satisfy the inequalityn2α2 ≤ (n2 − 1)δ + f 2, where ξ is the characteristic vector field,A is the shape operator and (n− 1)δ is the infimum of the Ricci curvatures of hypersurface M , then it is shown that α is a constant and ...

Abstract. We are concerned about the coarse and precise aspects of a priori estimates for Green’s function of a regular domain for the Laplacian-Betrami operator on any 3 ≤ n-dimensional complete non-compact boundary-free Riemannian manifold through the square Sobolev/Nash/logarithmic-Sobolev inequalities plus the rough and sharp Euclidean isoperimetric inequalities. Consequently, we are led to...

We find a unique torsion free Riemannian spin connection for the natural Killing metric on the quantum group Cq[SL2], using a recent frame bundle formulation. We find that its covariant Ricci curvature is essentially proportional to the metric (i.e. an Einstein space). We compute the Dirac operator D/ and find for q an odd r’th root of unity that its eigenvalues are given by q-integers [m]q for...

Torsion free connections and a notion of curvature are introduced on the in-nite dimensional nonlinear connguration space ? of a Riemannian manifold M under a Poisson measure. This allows to state identities of Weitzenbb ock type and energy identities for anticipating stochastic integral operators. The one-dimensional Poisson case itself gives rise to a non-trivial geometry, a de Rham-Hodge-Kod...

Let M be a compact (two-sided) minimal hypersurface in a Riemannian manifold M n+1 . It is a simple fact that if M has positive Ricci curvature then M cannot be stable (i. e. its Jacobi operator L has index at least one). If M = S(1) is the unit sphere and L has index one, then it is known that M must be a totally geodesic equator. We prove that if M is the real projective space RP = Sn+1(1)/{±...