Gravitational Chern-Simons Lagrangians and black hole entropy

We analyze the problem of defining the black hole entropy when Chern-Simons terms are present in the action. Extending previous works, we define a general procedure, valid in any odd dimensions both for purely gravitational CS terms and for mixed gauge-gravitational ones. The final formula is very similar to Wald's original formula valid for covariant actions, with a significant modification. Notwithstanding an apparent violation of covariance we argue that the entropy formula is indeed covariant.Comment: 39 page

Height estimates for Killing graphs

The paper aims at proving global height estimates for Killing graphs defined over a complete manifold with nonempty boundary. To this end, we first point out how the geometric analysis on a Killing graph is naturally related to a weighted manifold structure, where the weight is defined in terms of the length of the Killing vector field. According to this viewpoint, we introduce some potential theory on weighted manifolds with boundary and we prove a weighted volume estimate for intrinsic balls on the Killing graph. Finally, using these tools, we provide the desired estimate for the weighted height in the assumption that the Killing graph has constant weighted mean curvature and the weighted geometry of the ambient space is suitably controlled.Comment: 26 pages. Final version. To appear on Journal of Geometric Analysi

A classification of the torsion tensors on almost contact manifolds with B-metric

The space of the torsion (0,3)-tensors of the linear connections on almost contact manifolds with B-metric is decomposed in 15 orthogonal and invariant subspaces with respect to the action of the structure group. Three known connections, preserving the structure, are characterized regarding this classification.Comment: 17 pages, exposition clarified, references adde

Discrete moving frames on lattice varieties and lattice based multispace

In this paper, we develop the theory of the discrete moving frame in two different ways. In the first half of the paper, we consider a discrete moving frame defined on a lattice variety and the equivalence classes of global syzygies that result from the first fundamental group of the variety. In the second half, we consider the continuum limit of discrete moving frames as a local lattice coalesces to a point. To achieve a well-defined limit of discrete frames, we construct multispace, a generalization of the jet bundle that also generalizes Olver’s one dimensional construction. Using interpolation to provide coordinates, we prove that it is a manifold containing the usual jet bundle as a submanifold. We show that continuity of a multispace moving frame ensures that the discrete moving frame converges to a continuous one as lattices coalesce. The smooth frame is, at the same time, the restriction of the multispace frame to the embedded jet bundle. We prove further that the discrete invariants and syzygies approximate their smooth counterparts. In effect, a frame on multispace allows smooth frames and their discretisations to be studied simultaneously. In our last chapter we discuss two important applications, one to the discrete variational calculus, and the second to discrete integrable systems. Finally, in an appendix, we discuss a more general result concerning equicontinuous families of discretisations of moving frames, which are consistent with a smooth frame

Choline Dehydrogenase Polymorphism rs12676 Is a Functional Variation and Is Associated with Changes in Human Sperm Cell Function

Approximately 15% of couples are affected by infertility and up to half of these cases arise from male factor infertility. Unidentified genetic aberrations such as chromosomal deletions, translocations and single nucleotide polymorphisms (SNPs) may be the underlying cause of many cases of idiopathic male infertility. Deletion of the choline dehydrogenase (Chdh) gene in mice results in decreased male fertility due to diminished sperm motility; sperm from Chdh−/− males have decreased ATP concentrations likely stemming from abnormal sperm mitochondrial morphology and function in these cells. Several SNPs have been identified in the human CHDH gene that may result in altered CHDH enzymatic activity. rs12676 (G233T), a non-synonymous SNP located in the CHDH coding region, is associated with increased susceptibility to dietary choline deficiency and risk of breast cancer. We now report evidence that this SNP is also associated with altered sperm motility patterns and dysmorphic mitochondrial structure in sperm. Sperm produced by men who are GT or TT for rs12676 have 40% and 73% lower ATP concentrations, respectively, in their sperm. rs12676 is associated with decreased CHDH protein in sperm and hepatocytes. A second SNP located in the coding region of IL17BR, rs1025689, is linked to altered sperm motility characteristics and changes in choline metabolite concentrations in sperm