Future geodesic completeness of some spatially homogeneous solutions of the vacuum Einstein equations in higher dimensions

It is known that all spatially homogeneous solutions of the vacuum Einstein equations in four dimensions which exist for an infinite proper time towards the future are future geodesically complete. This paper investigates whether the analogous statement holds in higher dimensions. A positive answer to this question is obtained for a large class of models which can be studied with the help of Kaluza-Klein reduction to solutions of the Einstein-scalar field equations in four dimensions. The proof of this result makes use of a criterion for geodesic completeness which is applicable to more general spatially homogeneous models.Comment: 18 page

Percutaneous Anorectoplasty (PARP)-An Adaptable, Minimal-Invasive Technique for Anorectal Malformation Repair

Background: Anorectal malformations comprise a broad spectrum of disease. We developed a percutaneous anorectoplasty (PARP) technique as a minimal-invasive option for repair of amenable types of lesions. Methods: Patients who underwent PARP at five institutions from 2008 through 2021 were retrospectively analyzed. Demographic information, details of the operative procedure, and perioperative complications and outcomes were collected. Results: A total of 10 patients underwent the PARP procedure during the study interval. Patients either had low perineal malformations or no appreciable fistula. Most procedures were guided by ultrasound, fluoroscopy, or endoscopy. Median age at PARP was 3 days (range 1 to 311) days;eight patients were male. Only one intraoperative complication occurred, prompting conversion to posterior sagittal anorectoplasty. Functional outcomes in most children were highly satisfactory in terms of continence and functionality. Conclusions: The PARP technique is an excellent minimal-invasive alternative for boys born with perineal fistulae, as well as patients of both sexes without fistulae. The optimal type of guidance (ultrasound, fluoroscopy, or endoscopy) depends on the anatomy of the lesion and the presence of a colostomy at the time of repair

Future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI0_0

Using the methods developed for the Bianchi I case we have shown that a boostrap argument is also suitable to treat the future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI$_0$. These solutions are asymptotic to the Collins-Stewart solution with dust and the Ellis-MacCallum solution respectively. We have thus generalized the results obtained by Rendall and Uggla in the case of locally rotationally symmetric Bianchi II spacetimes to the reflection symmetric case. However we needed to assume small data. For Bianchi VI$_0$ there is no analogous previous result.Comment: 30 page