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We generalize Ringström's global future causal stability results [14] for certain expanding cosmological solutions of the Einstein-scalar field equations to solutions of the Einstein-Maxwell-scalar field system. In particular, after noting that the power law inflationary spacetimes (M n+1 ,ĝ,φ) considered by Ringström in [14] are solutions of the Einstein-Maxwell-scalar field system (with exponential potential) as well as of the Einstein-scalar field system (with the same exponential potential), we consider (nonlinear) perturbations of initial data sets of these spacetimes which include electromagnetic perturbations as well as gravitational and scalar perturbations. We show that if (as in [14]) we focus on pairs of relatively scaled open sets U R 0 ⊂ U 4R 0 on an initial slice of (M n+1 ,ĝ), and if we choose a set of perturbed data which on U 4R 0 is sufficiently close to that of (M n+1 ,ĝ,φ, = 0), then in the maximal globally hyperbolic spacetime development (M n+1 , g, φ, A) of this data via the Einstein-Maxwell-scalar field equations, all causal geodesics emanating from U R 0 are future complete (just as in (M n+1 ,ĝ)). We also verify the controlled future asymptotic behavior of the fields in the spacetime developments of the perturbed data sets.

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Objectives Development of endovenous treatment and sclerotherapy technology makes it feasible for clinicians to treat varicose veins (VV) through day surgery (DS). Superficial venous thrombosis (SVT) of lower extremities is a common complication of VV. This study aimed to investigate whether the existence of SVT below knee affect the safety and efficacy of DS for VV patients. Methods This is a single-center retrospective study. Clinical data of 593 VV patients was retrospectively analyzed. Raw data were matched by the using of propensity score matching model. Operation time, technical failure, postoperative DVT, skin burns, saphenous nerve injury, subcutaneous induration, and bleeding were compared between the groups. Also, we compared VV recurrence, SVT formation, DVT events and the change of VCSS score with 12 months. Results Fifty-nine patients complicated with SVT below knee were matched with 118 patients had VV only. Perioperative and follow-up outcomes were similar in both groups except for the number of incisions (median = 6 [5, 7] VS median = 4 [4, 5], P < 0.001). Both groups experienced a great decrease in VCSS score. Conclusion We systematically compared the clinical outcomes of DS in VV patients. Our results indicate DS is safe and effective for patients with VV, whether accompanied by SVT below the knee. Trial registration The ClinicalTrials.gov identifier for this trial is NCT05380895 (retrospectively registered).