a b s t r a c tProstaglandin F2a (PGF) treatment is routinely used in the reproductive management of mares to induce luteolysis and allow a subsequent return to estrus. The objective of this retrospective study was to assess the effect of follicle size at the time of administration of cloprostenol on interval to subsequent ovulation. A secondary objective was to determine the incidence of hemorrhagic anovulatory follicle (HAF) formation after PGF administration. Reproductive records of 275 mares monitored over a total of 520 estrous cycles were evaluated. All mares received a single intramuscular dose of 250 mg of the synthetic PGF analog cloprostenol sodium between days 5 and 12 after ovulation. The average interval from PGF to ovulation was 8.4 AE 2.5 days. The interval from PGF administration to subsequent ovulation was inversely proportional to the diameter of the largest follicle at the time of treatment. Administration of cloprostenol to mares with a large (!35 mm in diameter) diestrous follicle resulted in one of three outcomesdovulation within 48 hours (13.4%) with variable uterine edema, ovulation after 48 hours usually accompanied by the presence of uterine edema (73.1%), or regression without ovulation followed by emergence and eventual ovulation of a new dominant follicle (13.4%). There was no effect of mare age or season on interval from PGF to ovulation. The overall incidence of HAF development after PGF administration in this study was low (2.5%).

Abstract. On a hyperbolic Poincaré manifold, we derive an explicit relationship between the eigenvalues of Weyl-Schouten tensor of a conformal representative of the conformal infinity and the principal curvatures of the level sets of the associated geodesic defining function. This considerably simplifies the arguments and generalizes the results of Gálvez, Mira and the second author. In particular, we obtain the equivalence between Christoffel-type problems for hypersurfaces in a hyperbolic Poincaré manifold and scalar curvature problems on the conformal infinity.

In this paper we take an approach similar to that in [13] to establish a positive mass theorem for spin asymptotically hyperbolic manifolds admitting corners along a hypersurface. The main analysis uses an integral representation of a solution to a perturbed eigenfunction equation to obtain an asymptotic expansion of the solution in the right order. This allows us to understand the change of the mass aspect of a conformal change of asymptotically hyperbolic metrics.

Abstract. In [2], the authors develop a global correspondence between immersed weakly horospherically convex hypersurfaces φ : M n → H n+1 and a class of conformal metrics on domains of the round sphere S n . Some of the key aspects of the correspondence and its consequences have dimensional restrictions n ≥ 3 due to the reliance on an analytic proposition from [5] concerning the asymptotic behavior of conformal factors of conformal metrics on domains of S n . In this paper, we prove a new lemma about the asymptotic behavior of a functional combining the gradient of the conformal factor and itself, which allows us to extend the global correspondence and embeddedness theorems of [2] to all dimensions n ≥ 2 in a unified way. In the case of a single point boundary ∂ ∞ φ(M ) = {x} ⊂ S n , we improve these results in one direction.

A rigidity result for weakly asymptotically hyperbolic manifolds with lower bounds on Ricci curvature is proved without assuming that the manifolds are spin. The argument makes use of a quasi-local mass characterization of Euclidean balls from [9] [14] and eigenfunction compactification ideas from [12].