Existence and non-existence of cohomogeneity one Einstein metrics

This paper derives sufficient conditions for the existence and non-existence of cohomogeneity one Einstein metrics on double disk bundles of two summands type. These conditions are inequalities that only involve geometric data from the principal orbits. The existence theorem yields five infinite families and ten other sporadic examples of new inhomogeneous Einstein metrics. The non-existence theorem yields five examples whose principal orbits admit invariant Einstein metrics

On the Exhaustion of Local Remedies: Reconciling Sovereignty and Justice Before the European Court of Human Rights

Europe has a rule of law crisis. In the past decade, Turkey, Poland, and Hungary have undermined their democratic societies and compromised the independence of their institutions by affording unprecedented strength to their executive branch and imposing severe restrictions on the public sphere. As their illiberal policies spread, so does the frequency with which individuals adversely affected by these policies seek justice before the European Court of Human Rights. In these cases, Article 35(1) of the European Convention on Human Rights requires that they first exhaust the local remedies available in their national legal system. Article 35(1) reflects the role of the European Court of Human Rights to act as a subsidiary to Europe’s national judicial institutions and exercise a margin of appreciation for their ability to deliver a just outcome to litigants. However, this Comment shows that the principle of subsidiarity and the Court’s margin of appreciation for sovereign interests have led to an excessively formalistic interpretation of Article 35(1) in cases brought against Turkey and Hungary, leading to unjust conclusions for applicants and undermining the Court’s ability to guard against the erosion of rule of law in illiberal democracies. If the Court is to preserve its legitimacy as an institution capable of addressing human rights violations wherever they occur within its jurisdiction, it is critical that it plays a more active role in tackling Europe’s rule of law crisis. On this matter, Article 18 offers insight into the means by which the Court can provide relief to applicants and confront any unlawfully implemented state restrictions that compromise democratic governance in Member States without entirely delegitimizing these States’ legal and political systems

Positive Einstein Metrics with S4m+3\mathbb{S}^{4m+3} as Principal Orbit

We prove that there exists at least one positive Einstein metric on $\mathbb{HP}^{m+1}\sharp \overline{\mathbb{HP}}^{m+1}$ for $m\geq 2$. Based on the existence of the first Einstein metric, we give a criterion to check the existence of a second Einstein metric on $\mathbb{HP}^{m+1}\sharp \overline{\mathbb{HP}}^{m+1}$. We also investigate the existence of cohomogeneity one positive Einstein metrics on $\mathbb{S}^{4m+4}$ and prove the existence of a non-standard Einstein metric on $\mathbb{S}^8$

The UN’s Political Engagement in the Occupied Palestinian Territories: Reconceptualized Strategies in Humanitarianism and Diplomacy in the Middle East Peace Process

This paper studies the humanitarian crisis in the occupied Palestinian territories, focusing on the Palestinians’ short-term needs in emergency relief as well as their long-term needs regarding sustainable development, good governance, legal and physical protection. Against the backdrop of a cost/benefit analysis of the current UN humanitarian operational model, the paper then introduces new models of engagement, such the UN’s positioning itself as a mediator between the PA and the civic society throughout the implementation of a decentralized development model. Within this framework, the UN is advised to complement its engagement by facilitating negotiations towards a unified Palestinian government that incorporates the PA’s expertise in engaging the global political platform with the civic-based authority Hamas has within Palestine. The paper also proposes that the UN deploy a peace-keeping mission to help reduce the rate at which Israeli authorities and extremist settlers are pursuing a coercive environment in the WBGS. The last section of the essay highlights a reconceptualized diplomatic negotiation process spearheaded by the UN that complements its domestic operations. This reform essentially involves the expansion of the UN agenda to leverage the strategic partnerships the Gulf States, China, and Japan have with Israel and Palestine, as well as their financial powers to help sustain a viable Palestine until a settlement is reached

Decomposable (5, 6)-solutions in eleven-dimensional supergravity

We present decomposable (5, 6)-solutions M1,4×M6 in eleven-dimensional supergravity by solving the bosonic supergravity equations for a variety of non-trivial flux forms. Many of the bosonic backgrounds presented here are induced by various types of null flux forms on products of certain totally Ricci-isotropic Lorentzian Walker manifolds and Ricci-flat Riemannian manifolds. These constructions provide an analogy of the work performed by Chrysikos and Galaev [Classical Quantum Gravity 37, 125004 (2020)], who made similar computations for decomposable (6, 5)-solutions. We also present bosonic backgrounds that are products of Lorentzian Einstein manifolds with a negative Einstein constant (in the “mostly plus” convention) and Riemannian Kähler–Einstein manifolds with a positive Einstein constant. This conclusion generalizes a result of Pope and van Nieuwenhuizen [Commun. Math. Phys. 122, 281–292 (1989)] concerning the appearance of six-dimensional Kähler–Einstein manifolds in eleven-dimensional supergravity. In this setting, we construct infinitely many non-symmetric decomposable (5, 6)-supergravity backgrounds by using the infinitely many Lorentzian Einstein–Sasakian structures with a negative Einstein constant on the 5-sphere, known from the work of Boyer et al. [Commun. Math. Phys. 262, 177–208 (2006)]